There are quite some papers study on the GARCH models.
From previous papers, I tried to apply couple models for FOREX price forecasting and eventually got to know Fractional Intergrated GJR-GARCH is the best fit model as we can refer to GARCH模型中的ARMA(p,d,q)参数最优化1. Due to I simulate whole dataset to get the result in menmtioned paper is time consuming, I tried to apply dccroll() to know the mse by resampling but not only based on single AIC2. I parse my mv_fx() function3 and tested the Binary-Q1 - Multivariate GARCH Models and some additive parameters might probably need to be adjusted in the arguments of the function. Arma Part Overfitting in Arma Garch Model fitting via fGarch Package is a similar study for models comparison in GARCH.
I try to use 3 methods to compare the GARCH models.
forecast.length = 500, refit.every = 25, refit.window = 'recursive': refit couple times in order to make sure the stability of the prediction model.n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving': refit once only with moving to know the prediction accuracy of the Markov model.ugarchfit() and ugarchforecast() and save every single observation. It will be easy to find the origin of error and rerun that particular data prediction.Besides using the ugarchroll(), all models in this paper are Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q. AMATH546 - ECON589 HW3 also teach the use of ugarchroll().
## --- eval=FALSE, not run but display chunk ---
mv_fx <- function(...) {
...
mod = dccroll(dccSpec, data = mbase, solver = .solver,
forecast.length = 50, cluster = cl)
cat('step 1/1 dccroll done!\n')
...
}
cl = makePSOCKcluster(ncol(mbase))
## Workable
test_roll <- dccroll(dccspec(
multispec(c(ugarchspec(), ugarchspec(), ugarchspec(),
ugarchspec(), ugarchspec(), ugarchspec(),
ugarchspec())), distribution = 'mvt'),
data = mbase, cluster = cl)
## Not workable
test_roll2 <- dccroll(dccspec(
multispec(c(
uspec1 = ugarchspec(variance.model = list(model = 'gjrGARCH')),
uspec2 = ugarchspec(variance.model = list(model = 'gjrGARCH')),
uspec3 = ugarchspec(variance.model = list(model = 'gjrGARCH')),
uspec4 = ugarchspec(variance.model = list(model = 'gjrGARCH')),
uspec5 = ugarchspec(variance.model = list(model = 'gjrGARCH')),
uspec6 = ugarchspec(variance.model = list(model = 'gjrGARCH')),
uspec7 = ugarchspec(variance.model = list(model = 'gjrGARCH'))
))), data = mbase, cluster = cl)
#Error in checkForRemoteErrors(val) :
# one node produced an error: infinite or missing values in 'x'
## Workable
test_roll3 <- dccroll(dccspec(
multispec(c(
uspec1 = ugarchspec(
variance.model = list(model = 'eGARCH'),
distribution.model = 'snorm'),
uspec2 = ugarchspec(
variance.model = list(model = 'eGARCH'),
distribution.model = 'snorm'),
uspec3 = ugarchspec(
variance.model = list(model = 'eGARCH'),
distribution.model = 'snorm'),
uspec4 = ugarchspec(
variance.model = list(model = 'eGARCH'),
distribution.model = 'snorm'),
uspec5 = ugarchspec(
variance.model = list(model = 'eGARCH'),
distribution.model = 'snorm'),
uspec6 = ugarchspec(
variance.model = list(model = 'eGARCH'),
distribution.model = 'snorm'),
uspec7 = ugarchspec(
variance.model = list(model = 'eGARCH'),
distribution.model = 'snorm')
)), distribution = 'mvt'), data = mbase, cluster = cl)
## Not workable
test_roll4 <- dccroll(dccspec(
multispec(c(
uspec1 = ugarchspec(
variance.model = list(model = 'gjrGARCH'),
distribution.model = 'snorm'),
uspec2 = ugarchspec(
variance.model = list(model = 'gjrGARCH'),
distribution.model = 'snorm'),
uspec3 = ugarchspec(
variance.model = list(model = 'gjrGARCH'),
distribution.model = 'snorm'),
uspec4 = ugarchspec(
variance.model = list(model = 'gjrGARCH'),
distribution.model = 'snorm'),
uspec5 = ugarchspec(
variance.model = list(model = 'gjrGARCH'),
distribution.model = 'snorm'),
uspec6 = ugarchspec(
variance.model = list(model = 'gjrGARCH'),
distribution.model = 'snorm'),
uspec7 = ugarchspec(
variance.model = list(model = 'gjrGARCH'),
distribution.model = 'snorm')
)), distribution = 'mvt'), data = mbase, cluster = cl)
#Error in checkForRemoteErrors(val) :
# one node produced an error: infinite or missing values in 'x'
Binary-Q14 compares all possible GARCH models in rugarch package while the result is in ROI (Return on Investment), due to the paper Binary-Q1 - Tick-Data-HiLo For Daily Trading (Blooper) found that the betting strategy is not workable in real-life. Therefore I try to compare again the GARCH models as well as suite for multivariate GARCH models.
Due to the multivartiate models will not coped with every univariate models. Here I tried to compare the accuracy of forecasting by univariate GARCH models and later will compare with the multivariate models.
Similar with GARCH模型中的ARMA(p,d,q)参数最优化, I use the dataset from Binary-Q1 (Extention)5 to ease the study.
cr_code <- c('AUDUSD=X', 'EURUSD=X', 'GBPUSD=X', 'CHF=X', 'CAD=X',
'CNY=X', 'JPY=X')
#'@ names(cr_code) <- c('AUDUSD', 'EURUSD', 'GBPUSD', 'USDCHF', 'USDCAD',
#'@ 'USDCNY', 'USDJPY')
names(cr_code) <- c('USDAUD', 'USDEUR', 'USDGBP', 'USDCHF', 'USDCAD', 'USDCNY', 'USDJPY')
## Read presaved Yahoo data.
mbase <- sapply(names(cr_code), function(x) readRDS(paste0('./data/', x, '.rds')) %>% na.omit)
price_type <- c('Op', 'Hi', 'Lo', 'Cl')
gmds <- c('sGARCH', 'fGARCH.GARCH', 'fGARCH.TGARCH', 'fGARCH.AVGARCH', 'fGARCH.NGARCH', 'fGARCH.NAGARCH', 'fGARCH.APARCH', 'fGARCH.GJRGARCH', 'fGARCH.ALLGARCH', 'eGARCH', 'gjrGARCH', 'apARCH', 'iGARCH', 'csGARCH')
timeID <- llply(mbase, function(x) as.character(index(x))) %>%
unlist %>% unique %>% as.Date %>% sort
timeID <- c(timeID, xts::last(timeID) + days(1)) #the last date + 1 in order to predict the next day of last date to make whole dataset completed.
timeID0 <- ymd('2013-01-01')
timeID <- timeID[timeID >= timeID0]
.cl = FALSE
All my previous papers applied Markov theory which is \(p(x_{n}|x_{n-1}...x_{1})\), here I try to test if the model provides same result. Here I iteration 100 times.
## ================ eval=FALSE ====================
## sample data.
x <- mbase[['USDJPY']] %>% Cl
armaOrder = opt_arma(x)
spec = ugarchspec(
variance.model = list(
model = 'sGARCH', garchOrder = c(1, 1),
submodel = NULL, external.regressors = NULL,
variance.targeting = FALSE),
mean.model = list(
armaOrder = armaOrder[c(1, 3)],
include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = TRUE,
external.regressors = NULL,
archex = FALSE),
fixed.pars = list(arfima = armaOrder[2]),
distribution.model = 'snorm')
fit <- ugarchfit(spec, x, solver = 'hybrid')
## Execute 1 times.
fc1 = ugarchforecast(fit, n.ahead = 1)
## Execute 100 times to know if the coffecient value is applied ML method.
fc2 = replicate(100, ugarchforecast(fit, n.ahead = 1))
## retrieve the series and sigma values.
fc1 <- cbind(attributes(fc1)$`forecast`$seriesFor, attributes(fc1)$`forecast`$sigmaFor)
fc2 <- llply(fc2, function(x) cbind(attributes(x)$`forecast`$seriesFor, attributes(x)$`forecast`$sigmaFor)) %>% do.call('rbind', .)
fc2 %<>% unique
#> rbind(fc1, fc2)
# 2017-08-30 2017-08-30
#T+1 110.4566 0.6523954
#T+1 110.4566 0.6523954
#> fc1 == fc2
# 2017-08-30 2017-08-30
#T+1 TRUE TRUE
rm(x)
From above test, we know that the prediction price is exactly same upon testing 100 times.
Below is the backtest simulation. The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive' which only apply Monte Carlo method to resampling the model.
if (!file.exists('data/fx/mse.sGARCH.rds')) {
mse.sGARCH <- ldply(mbase, function(x) {
x <- Cl(x)
if (.cl == TRUE) {
.cl <- makePSOCKcluster(ncol(x))
} else {
.cl <- NULL
}
armaOrder = opt_arma(x)
spec = ugarchspec(
variance.model = list(
model = 'sGARCH', garchOrder = c(1, 1),
submodel = NULL, external.regressors = NULL,
variance.targeting = FALSE),
mean.model = list(
armaOrder = armaOrder[c(1, 3)],
include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = TRUE,
external.regressors = NULL,
archex = FALSE),
fixed.pars = list(arfima = armaOrder[2]),
distribution.model = 'snorm')
roll <- ugarchroll(spec, data = x, refit.window = 'recursive',
cluster = .cl)
res <- attributes(roll)$forecast$density
if (!is.null(res)) {
res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>%
.$MSE %>% unique
} else {
res <- NULL
}
return(res)
}) %>% tbl_df
#'@ names(mse.sGARCH)[2] <- 'MSE'
mse.sGARCH %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
saveRDS(mse.sGARCH, 'data/fx/mse.sGARCH.rds')
} else {
mse.sGARCH <- readRDS('data/fx/mse.sGARCH.rds')
}
mse.sGARCH %>%
rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2]))) %>%
kable(caption = 'MSE for Univariate sGARCH') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 0.0000717 |
| 2 | USDEUR | 0.0000232 |
| 3 | USDGBP | 0.0000277 |
| 4 | USDCHF | 0.0000267 |
| 5 | USDCAD | 0.0000466 |
| 6 | USDCNY | 0.0002822 |
| 7 | USDJPY | 0.5196658 |
| MSE | Mean | 0.0743063 |
Table 3.1.1A : MSE of basket currencies.
By refer to below article, I use ugarchroll() which is a wrapper for ugarchfit() and ugarchforecast() which will made the thing use :
There has a concern to use it which is once there has an error during the course of simulation will cause whole data gone.6 All my previous preditive result based on the Markov Chain theory7 with statistical modelling and prediction model and saved every single predictive result.
Below is the simulation . n.start = ns is the start point of simulation which is ymd('2013-01-01'), forecast.length = nrow(x) - ns is the length of forecast equal to the length from the n.start until the end of the dataset, refit.every = 1 means re-estimate the fit value once only where refit.window = 'moving' where today’s dataset only can predict 1 trading day in advance.
## --- eval=FALSE ---- Due to errors.
if (!file.exists('data/fx/mse.sGARCH2.rds')) {
mse.sGARCH2 <- ldply(mbase, function(x) {
x <- Cl(x)
if (.cl == TRUE) {
.cl <- makePSOCKcluster(ncol(x))
} else {
.cl <- NULL
}
armaOrder = opt_arma(x)
spec = ugarchspec(
variance.model = list(
model = 'sGARCH', garchOrder = c(1, 1),
submodel = NULL, external.regressors = NULL,
variance.targeting = FALSE),
mean.model = list(
armaOrder = armaOrder[c(1, 3)],
include.mean = TRUE, archm = FALSE,
archpow = 1, arfima = TRUE,
external.regressors = NULL,
archex = FALSE),
fixed.pars = list(arfima = armaOrder[2]),
distribution.model = 'snorm')
ns <- which(index(x) == timeID0)
n <- nrow(x) - ns
roll <- ugarchroll(spec, data = x, n.start = ns, forecast.length = n,
refit.every = 1, refit.window = 'moving',
cluster = .cl)
res <- attributes(roll)$forecast$density
if (!is.null(res)) {
res %>% tbl_df %>% mutate(MSE = mean((Mu - Realized)^2)) %>%
.$MSE %>% unique
} else {
res <- NULL
}
return(res)
}) %>% tbl_df
mse.sGARCH2 %<>% ddply(.(.id), summarise, MSE = mean((Mu - Realized)^2))
saveRDS(mse.sGARCH2, 'data/fx/mse.sGARCH2.rds')
} else {
mse.sGARCH2 <- readRDS('data/fx/mse.sGARCH2.rds')
}
if (!is.null(mse.sGARCH2)) {
mse.sGARCH2 %>%
rbind(., data.frame(.id = 'Mean', MSE = colMeans(.[2]))) %>%
kable(caption = 'MSE for Univariate sGARCH') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
}
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 6.250000e-05 |
| 2 | USDCAD | 4.524806e+131 |
| 3 | USDCHF | 5.310000e-05 |
| 4 | USDCNY | 1.839000e-04 |
| 5 | USDEUR | 2.330000e-05 |
| 6 | USDGBP | 1.660000e-05 |
| 7 | USDJPY | 4.885790e-01 |
| MSE | Mean | 6.464009e+130 |
Table 3.1.1B : MSE of basket currencies.
Due to I am not statisfy and doubted onto the AIC result based on model comparison by using basic model above. Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q to proof if my previous study8 in Binary.com Interview Q1 is correct.
Binary.com Interview Q1 - Tick-Data-HiLo For Daily Trading (Blooper) directly use the mentioned gjrGARCH model but add another criteria which is the timing of daily High-Low price based on highest bid and lowest ask price within a day.
## ------------- Simulate uv_fx() ----------------------
## uv_fx just made the model and some argument flexible.
sGARCH <- list()
for (dt in timeID) {
for (i in seq(cr_code)) {
smp <- mbase[[names(cr_code)[i]]]
timeID2 <- c(index(smp), xts::last(index(smp)) + days(1))
if (dt %in% timeID2) {
dtr <- xts::last(index(smp[index(smp) < dt]), 1) #tail(..., 1)
smp <- smp[paste0(dtr %m-% years(1), '/', dtr)]
sGARCH[[i]] <- tryCatch({ldply(price_type, function(y) {
df = uv_fx(smp, .model = 'sGARCH', currency = cr_code[i],
price = y, .cluster = .cl)
df = data.frame(Date = index(df$latestPrice[1]),
Type = paste0(names(df$latestPrice), '.', y),
df$latestPrice, df$forecastPrice, t(df$AIC))
names(df)[4] %<>% str_replace_all('1', 'T+1')
df
})}, error = function(e) NULL)
if (!dir.exists(paste0('data/fx/', names(sGARCH[[i]])[3])))
dir.create(paste0('data/fx/', names(sGARCH[[i]])[3]))
saveRDS(sGARCH[[i]], paste0(
'data/fx/', names(sGARCH[[i]])[3], '/sGARCH.',
unique(sGARCH[[i]]$Date), '.rds'))
cat(paste0(
'data/fx/', names(sGARCH[[i]])[3], '/sGARCH.',
unique(sGARCH[[i]]$Date), '.rds saved!\n'))
}
}; rm(i)
}
The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 0.0000717 |
| 2 | USDEUR | 0.0000232 |
| 3 | USDGBP | 0.0000277 |
| 4 | USDCHF | 0.0000267 |
| 5 | USDCAD | 0.0000469 |
| 6 | USDCNY | 0.0002822 |
| 7 | USDJPY | NA |
| MSE | Mean | 0.0000797 |
Table 3.2.1.1A : MSE of basket currencies.
Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 6.250000e-05 |
| 2 | USDCAD | 6.449515e+178 |
| 3 | USDCHF | 5.300000e-05 |
| 4 | USDCNY | 1.839000e-04 |
| 5 | USDEUR | 2.330000e-05 |
| 6 | USDGBP | 1.660000e-05 |
| 7 | USDJPY | 4.895937e-01 |
| MSE | Mean | 9.213592e+177 |
Table 3.2.1.1B : MSE of basket currencies.
Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.
The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 0.0000719 |
| 2 | USDCAD | 0.0000470 |
| 3 | USDCHF | 0.0000249 |
| 4 | USDEUR | 0.0000232 |
| 5 | USDGBP | 0.0000277 |
| 6 | USDJPY | 0.5291517 |
| MSE | Mean | 0.0882244 |
Table 3.2.2.1A : MSE of basket currencies.
Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.
| .id | MSE | |
|---|---|---|
| 1 | USDJPY | 0.4901144 |
| MSE | Mean | 0.4901144 |
Table 3.2.2.1B : MSE of basket currencies.
Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.
The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 0.0000718 |
| 2 | USDCAD | 0.0000473 |
| 3 | USDCHF | 0.0000259 |
| 4 | USDEUR | 0.0000233 |
| 5 | USDGBP | 0.0000277 |
| 6 | USDJPY | 0.5321997 |
| MSE | Mean | 0.0887326 |
Table 3.2.3.1A : MSE of basket currencies.
Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.
Table 3.2.3.1B : MSE of basket currencies.
Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.
The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 0.0000719 |
| 2 | USDCAD | 0.0000469 |
| 3 | USDCHF | 0.0000250 |
| 4 | USDCNY | 0.0002831 |
| 5 | USDEUR | 0.0000232 |
| 6 | USDGBP | 0.0000277 |
| 7 | USDJPY | 0.5222741 |
| MSE | Mean | 0.0746788 |
Table 3.2.4.1A : MSE of basket currencies.
Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.
| .id | MSE | |
|---|---|---|
| 1 | USDCHF | 0.0000682 |
| 2 | USDCNY | 0.0001853 |
| 3 | USDEUR | 0.0000235 |
| MSE | Mean | 0.0000924 |
Table 3.2.4.1B : MSE of basket currencies.
Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.
The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 0.0000717 |
| 2 | USDCAD | 0.0000469 |
| 3 | USDCHF | 0.0000237 |
| 4 | USDCNY | 0.0002824 |
| 5 | USDEUR | 0.0000232 |
| 6 | USDGBP | 0.0000277 |
| MSE | Mean | 0.0000792 |
Table 3.2.5.1A : MSE of basket currencies.
Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.
| .id | MSE | |
|---|---|---|
| 1 | USDCNY | 0.0001836 |
| MSE | Mean | 0.0001836 |
Table 3.2.5.1B : MSE of basket currencies.
Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.
The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 0.0000717 |
| 2 | USDCHF | 0.0000259 |
| 3 | USDEUR | 0.0000232 |
| 4 | USDJPY | 0.5236997 |
| MSE | Mean | 0.1309551 |
Table 3.2.6.1A : MSE of basket currencies.
Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.
Table 3.2.6.1B : MSE of basket currencies.
Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.
The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 7.17e-05 |
| 2 | USDCAD | 4.68e-05 |
| 3 | USDCHF | 2.41e-05 |
| 4 | USDCNY | 2.82e-04 |
| 5 | USDEUR | 2.32e-05 |
| 6 | USDGBP | 2.77e-05 |
| MSE | Mean | 7.93e-05 |
Table 3.2.7.1A : MSE of basket currencies.
Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.
| .id | MSE | |
|---|---|---|
| 1 | USDGBP | 0.0000166 |
| 2 | USDJPY | 0.4880047 |
| MSE | Mean | 0.2440106 |
Table 3.2.7.1B : MSE of basket currencies.
Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.
The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 0.0000717 |
| 2 | USDEUR | 0.0000232 |
| 3 | USDGBP | 0.0000277 |
| 4 | USDCHF | 0.0000236 |
| 5 | USDCAD | 0.0000470 |
| 6 | USDCNY | 0.0002821 |
| 7 | USDJPY | 0.5237676 |
| MSE | Mean | 0.0748918 |
Table 3.2.8.1A : MSE of basket currencies.
Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.
Table 3.2.8.1B : MSE of basket currencies.
Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.
The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 0.0000717 |
| 2 | USDCAD | 0.0000469 |
| 3 | USDCHF | 0.0000236 |
| 4 | USDCNY | 0.0002793 |
| 5 | USDEUR | 0.0000232 |
| 6 | USDGBP | 0.0000277 |
| 7 | USDJPY | 0.5199591 |
| MSE | Mean | 0.0743473 |
Table 3.3.1A : MSE of basket currencies.
Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.
Table 3.3.1B : MSE of basket currencies.
Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.
The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 0.0000717 |
| 2 | USDCAD | 0.0000470 |
| 3 | USDCHF | 0.0000242 |
| 4 | USDCNY | 0.0002820 |
| 5 | USDEUR | 0.0000232 |
| 6 | USDGBP | 0.0000277 |
| 7 | USDJPY | 0.5288255 |
| MSE | Mean | 0.0756145 |
Table 3.4.1A : MSE of basket currencies.
Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 6.280000e-05 |
| 2 | USDCAD | 3.590000e-05 |
| 3 | USDCHF | 4.990000e-05 |
| 4 | USDCNY | 2.277193e+142 |
| 5 | USDEUR | 2.340000e-05 |
| 6 | USDGBP | 1.660000e-05 |
| 7 | USDJPY | 4.881093e-01 |
| MSE | Mean | 3.253132e+141 |
Table 3.4.1B : MSE of basket currencies.
Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.
Here I do not execute this model but directly read the previous dataset due to it is the model pred2 in GARCH模型中的ARMA(p,d,q)参数最优化.
The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 0.0000718 |
| 2 | USDCAD | 0.0000472 |
| 3 | USDCNY | 0.0002826 |
| 4 | USDEUR | 0.0000294 |
| 5 | USDGBP | 0.0000277 |
| 6 | USDJPY | 0.5229902 |
| MSE | Mean | 0.0872415 |
Table 3.5.1A : MSE of basket currencies.
Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.
Table 3.5.1B : MSE of basket currencies.
Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.
The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 0.0000717 |
| 2 | USDCHF | 0.0000259 |
| 3 | USDCNY | 0.0002845 |
| 4 | USDEUR | 0.0000232 |
| 5 | USDGBP | 0.0000277 |
| 6 | USDJPY | 0.5238451 |
| MSE | Mean | 0.0873797 |
Table 3.6.1A : MSE of basket currencies.
Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.
Table 3.6.1B : MSE of basket currencies.
Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.
The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'.
| .id | MSE | |
|---|---|---|
| 1 | USDAUD | 0.0000717 |
| 2 | USDCHF | 0.0000259 |
| 3 | USDCNY | 0.0002817 |
| 4 | USDEUR | 0.0000232 |
| 5 | USDGBP | 0.0000277 |
| 6 | USDJPY | 0.5227716 |
| MSE | Mean | 0.0872003 |
Table 3.7.1A : MSE of basket currencies.
Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.
Table 3.7.1B : MSE of basket currencies.
Below I compared the Fractional Intergrated model which optimised the arfima q and also adjusted arma order p and q.
Due to some unknown reasons, the NGARCH and NAGARCH always bias to confuse the model selection. Here I try to look for some supportive methods.
By refer to How to Choose a Forecast for Your Time Series, here I calculated the AIC of MSE to choose the best fitted model.
\[AIC = 2k - 2log(L)\]
where \(k\) is the number of parameter, log is the logarithm and L is the likelihood function.
\[MSE = \sum_{i=1}^{n}(x_{i}-\mu_{i})^2\]
\[AIC = 2k+nlog(MSE)\]
Below picture shows the use of BIC for Markov model (as well as few parameters used in the model) while AIC for static model. For section Resampling Method, we can refer to AIC while section Markov Method and section Markov Method 2 we refer to BIC.
In order to know the stability of AIC value, here I try to measure the mean squared error of AIC as well.
As states, due to some unknown reasons, there has some data bias more than 100 times which is totally wrong. Some prediction price became AIC value and somemore the currency became NULL values after calculation.
Here I also filter and count the number of bias to pick the best fit model.
The default setting is forecast.length = 500, refit.every = 25, refit.window = 'recursive'. Below is the MSE summary for the models.
## remove all mse.*objects to save memory.
eval(parse(text = paste0('rm(\'', ls()[str_detect(ls(), 'mse.')],'\')')))
models <- llply(gmds, function(txt) {
readRDS(paste0('data/fx/mse.', txt, '.rds')) %>%
data.frame(Cat = txt, .)
})
names(models) <- gmds
models <- suppressAll(bind_rows(models)) %>% tbl_df %>%
mutate(Cat = factor(Cat), .id = factor(.id))
models %>% ddply(.(.id, Cat), summarise, MSE = mean(MSE, na.rm=TRUE)) %>%
kable(caption = 'Summary') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
group_rows('USD/AUD', 1, 14, label_row_css = 'background-color: #003399; color: #fff;') %>%
group_rows('USD/CAD', 15, 25, label_row_css = 'background-color: #003399; color: #fff;') %>%
group_rows('USD/CHF', 26, 38, label_row_css = 'background-color: #003399; color: #fff;') %>%
group_rows('USD/CNY', 39, 49, label_row_css = 'background-color: #003399; color: #fff;') %>%
group_rows('USD/EUR', 50, 63, label_row_css = 'background-color: #003399; color: #fff;') %>%
group_rows('USD/GBP', 64, 76, label_row_css = 'background-color: #003399; color: #fff;') %>%
group_rows('USD/JPY', 77, 88, label_row_css = 'background-color: #003399; color: #fff;') %>%
scroll_box(width = '100%', height = '400px')
| .id | Cat | MSE |
|---|---|---|
| USD/AUD | ||
| USDAUD | apARCH | 0.0000718 |
| USDAUD | csGARCH | 0.0000717 |
| USDAUD | eGARCH | 0.0000717 |
| USDAUD | fGARCH.ALLGARCH | 0.0000717 |
| USDAUD | fGARCH.APARCH | 0.0000717 |
| USDAUD | fGARCH.AVGARCH | 0.0000718 |
| USDAUD | fGARCH.GARCH | 0.0000717 |
| USDAUD | fGARCH.GJRGARCH | 0.0000717 |
| USDAUD | fGARCH.NAGARCH | 0.0000717 |
| USDAUD | fGARCH.NGARCH | 0.0000719 |
| USDAUD | fGARCH.TGARCH | 0.0000719 |
| USDAUD | gjrGARCH | 0.0000717 |
| USDAUD | iGARCH | 0.0000717 |
| USDAUD | sGARCH | 0.0000717 |
| USD/CAD | ||
| USDCAD | apARCH | 0.0000472 |
| USDCAD | eGARCH | 0.0000469 |
| USDCAD | fGARCH.ALLGARCH | 0.0000470 |
| USDCAD | fGARCH.AVGARCH | 0.0000473 |
| USDCAD | fGARCH.GARCH | 0.0000469 |
| USDCAD | fGARCH.GJRGARCH | 0.0000468 |
| USDCAD | fGARCH.NAGARCH | 0.0000469 |
| USDCAD | fGARCH.NGARCH | 0.0000469 |
| USDCAD | fGARCH.TGARCH | 0.0000470 |
| USDCAD | gjrGARCH | 0.0000470 |
| USDCAD | sGARCH | 0.0000466 |
| USD/CHF | ||
| USDCHF | csGARCH | 0.0000259 |
| USDCHF | eGARCH | 0.0000236 |
| USDCHF | fGARCH.ALLGARCH | 0.0000236 |
| USDCHF | fGARCH.APARCH | 0.0000259 |
| USDCHF | fGARCH.AVGARCH | 0.0000259 |
| USDCHF | fGARCH.GARCH | 0.0000267 |
| USDCHF | fGARCH.GJRGARCH | 0.0000241 |
| USDCHF | fGARCH.NAGARCH | 0.0000237 |
| USDCHF | fGARCH.NGARCH | 0.0000250 |
| USDCHF | fGARCH.TGARCH | 0.0000249 |
| USDCHF | gjrGARCH | 0.0000242 |
| USDCHF | iGARCH | 0.0000259 |
| USDCHF | sGARCH | 0.0000267 |
| USD/CNY | ||
| USDCNY | apARCH | 0.0002826 |
| USDCNY | csGARCH | 0.0002817 |
| USDCNY | eGARCH | 0.0002793 |
| USDCNY | fGARCH.ALLGARCH | 0.0002821 |
| USDCNY | fGARCH.GARCH | 0.0002822 |
| USDCNY | fGARCH.GJRGARCH | 0.0002820 |
| USDCNY | fGARCH.NAGARCH | 0.0002824 |
| USDCNY | fGARCH.NGARCH | 0.0002831 |
| USDCNY | gjrGARCH | 0.0002820 |
| USDCNY | iGARCH | 0.0002845 |
| USDCNY | sGARCH | 0.0002822 |
| USD/EUR | ||
| USDEUR | apARCH | 0.0000294 |
| USDEUR | csGARCH | 0.0000232 |
| USDEUR | eGARCH | 0.0000232 |
| USDEUR | fGARCH.ALLGARCH | 0.0000232 |
| USDEUR | fGARCH.APARCH | 0.0000232 |
| USDEUR | fGARCH.AVGARCH | 0.0000233 |
| USDEUR | fGARCH.GARCH | 0.0000232 |
| USDEUR | fGARCH.GJRGARCH | 0.0000232 |
| USDEUR | fGARCH.NAGARCH | 0.0000232 |
| USDEUR | fGARCH.NGARCH | 0.0000232 |
| USDEUR | fGARCH.TGARCH | 0.0000232 |
| USDEUR | gjrGARCH | 0.0000232 |
| USDEUR | iGARCH | 0.0000232 |
| USDEUR | sGARCH | 0.0000232 |
| USD/GBP | ||
| USDGBP | apARCH | 0.0000277 |
| USDGBP | csGARCH | 0.0000277 |
| USDGBP | eGARCH | 0.0000277 |
| USDGBP | fGARCH.ALLGARCH | 0.0000277 |
| USDGBP | fGARCH.AVGARCH | 0.0000277 |
| USDGBP | fGARCH.GARCH | 0.0000277 |
| USDGBP | fGARCH.GJRGARCH | 0.0000277 |
| USDGBP | fGARCH.NAGARCH | 0.0000277 |
| USDGBP | fGARCH.NGARCH | 0.0000277 |
| USDGBP | fGARCH.TGARCH | 0.0000277 |
| USDGBP | gjrGARCH | 0.0000277 |
| USDGBP | iGARCH | 0.0000277 |
| USDGBP | sGARCH | 0.0000277 |
| USD/JPY | ||
| USDJPY | apARCH | 0.5229902 |
| USDJPY | csGARCH | 0.5227716 |
| USDJPY | eGARCH | 0.5199591 |
| USDJPY | fGARCH.ALLGARCH | 0.5237676 |
| USDJPY | fGARCH.APARCH | 0.5236997 |
| USDJPY | fGARCH.AVGARCH | 0.5321997 |
| USDJPY | fGARCH.GARCH | NaN |
| USDJPY | fGARCH.NGARCH | 0.5222741 |
| USDJPY | fGARCH.TGARCH | 0.5291517 |
| USDJPY | gjrGARCH | 0.5288255 |
| USDJPY | iGARCH | 0.5238451 |
| USDJPY | sGARCH | 0.5196658 |
Due to some models unable produced a result, here I only filter and display the models with 7 currencies as below.
#'@ dplyr::count(models, Cat) %>% dplyr::filter(n == 7)
cats <- dplyr::count(models, Cat) %>% dplyr::filter(n == 7) %>% .[1] %>% unlist %>% factor
models %>% ddply(.(Cat), summarise, MSE = mean(MSE, na.rm=TRUE)) %>%
dplyr::filter(Cat %in% cats) %>%
kable(caption = 'Summary') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive'))
| Cat | MSE |
|---|---|
| eGARCH | 0.0743473 |
| fGARCH.ALLGARCH | 0.0748918 |
| fGARCH.GARCH | 0.0000797 |
| fGARCH.NGARCH | 0.0746788 |
| gjrGARCH | 0.0756145 |
| sGARCH | 0.0743063 |
Now I plot a table with rank where shows all possible models.
Set n.start = ns, forecast.length = nrow(x) - ns, refit.every = 1, refit.window = 'moving'.
| .id | Cat | MSE |
|---|---|---|
| USDAUD | fGARCH.GARCH | 6.250000e-05 |
| USDAUD | gjrGARCH | 6.280000e-05 |
| USDAUD | sGARCH | 6.250000e-05 |
| USDCAD | fGARCH.GARCH | 6.449515e+178 |
| USDCAD | gjrGARCH | 3.590000e-05 |
| USDCAD | sGARCH | 4.524806e+131 |
| USDCHF | fGARCH.GARCH | 5.300000e-05 |
| USDCHF | fGARCH.NGARCH | 6.820000e-05 |
| USDCHF | gjrGARCH | 4.990000e-05 |
| USDCHF | sGARCH | 5.310000e-05 |
| USDCNY | fGARCH.GARCH | 1.839000e-04 |
| USDCNY | fGARCH.NAGARCH | 1.836000e-04 |
| USDCNY | fGARCH.NGARCH | 1.853000e-04 |
| USDCNY | gjrGARCH | 2.277193e+142 |
| USDCNY | sGARCH | 1.839000e-04 |
| USDEUR | fGARCH.GARCH | 2.330000e-05 |
| USDEUR | fGARCH.NGARCH | 2.350000e-05 |
| USDEUR | gjrGARCH | 2.340000e-05 |
| USDEUR | sGARCH | 2.330000e-05 |
| USDGBP | fGARCH.GARCH | 1.660000e-05 |
| USDGBP | fGARCH.GJRGARCH | 1.660000e-05 |
| USDGBP | gjrGARCH | 1.660000e-05 |
| USDGBP | sGARCH | 1.660000e-05 |
| USDJPY | fGARCH.GARCH | 4.895937e-01 |
| USDJPY | fGARCH.GJRGARCH | 4.880047e-01 |
| USDJPY | fGARCH.TGARCH | 4.901144e-01 |
| USDJPY | gjrGARCH | 4.881093e-01 |
| USDJPY | sGARCH | 4.885790e-01 |
Due to some models unable produced a result, here I only filter and display the models with 7 currencies as below.
| Cat | MSE |
|---|---|
| fGARCH.GARCH | 9.213592e+177 |
| gjrGARCH | 3.253132e+141 |
| sGARCH | 6.464009e+130 |
Now I plot a table with rank where shows all possible models.
Now, we look at the mse where I use ugarchfit() and ugarchforecast, actually it is same with above Markov Method but just seperate all prediction result as single file where we able to filter the error to find the most accurate model (as well as know he frequence of bias and precise among the models.).
Below check the progress of the saved files.
## check how many data saved in progress.
l_ply(gmds, function(x) {
x2 <- ifelse(x == 'gjrGARCH', 'pred2', x)
task_progress(.pattern = paste0('^', x2, '.'), .loops = FALSE)
})
## Current Tokyo Time : 2018-08-25 23:27:30
## ^sGARCH.
##
## .id x n progress
## 1 USDAUD 1215 1215 100.00%
## 2 USDEUR 1215 1215 100.00%
## 3 USDGBP 1216 1216 100.00%
## 4 USDCHF 1214 1215 99.92%
## 5 USDCAD 1214 1214 100.00%
## 6 USDCNY 1214 1215 99.92%
## 7 USDJPY 1215 1215 100.00%
##
## ================ 99.98% ================
##
## Current Tokyo Time : 2018-08-25 23:27:31
## ^fGARCH.GARCH.
##
## .id x n progress
## 1 USDAUD 1214 1215 99.92%
## 2 USDEUR 1214 1215 99.92%
## 3 USDGBP 1215 1216 99.92%
## 4 USDCHF 1215 1215 100.00%
## 5 USDCAD 1214 1214 100.00%
## 6 USDCNY 1214 1215 99.92%
## 7 USDJPY 1215 1215 100.00%
##
## ================ 99.95% ================
##
## Current Tokyo Time : 2018-08-25 23:27:32
## ^fGARCH.TGARCH.
##
## .id x n progress
## 1 USDAUD 1203 1215 99.01%
## 2 USDEUR 1137 1215 93.58%
## 3 USDGBP 1200 1216 98.68%
## 4 USDCHF 1176 1215 96.79%
## 5 USDCAD 1181 1214 97.28%
## 6 USDCNY 1195 1215 98.35%
## 7 USDJPY 1213 1215 99.84%
##
## ================ 97.65% ================
##
## Current Tokyo Time : 2018-08-25 23:27:34
## ^fGARCH.AVGARCH.
##
## .id x n progress
## 1 USDAUD 78 1215 6.42%
## 2 USDEUR 45 1215 3.70%
## 3 USDGBP 56 1216 4.61%
## 4 USDCHF 19 1215 1.56%
## 5 USDCAD 62 1214 5.11%
## 6 USDCNY 13 1215 1.07%
## 7 USDJPY 61 1215 5.02%
##
## ================ 3.93% ================
##
## Current Tokyo Time : 2018-08-25 23:27:35
## ^fGARCH.NGARCH.
##
## .id x n progress
## 1 USDAUD 1199 1215 98.68%
## 2 USDEUR 1203 1215 99.01%
## 3 USDGBP 1202 1216 98.85%
## 4 USDCHF 1204 1215 99.09%
## 5 USDCAD 1196 1214 98.52%
## 6 USDCNY 1203 1215 99.01%
## 7 USDJPY 1198 1215 98.60%
##
## ================ 98.82% ================
##
## Current Tokyo Time : 2018-08-25 23:27:36
## ^fGARCH.NAGARCH.
##
## .id x n progress
## 1 USDAUD 1048 1215 86.26%
## 2 USDEUR 1025 1215 84.36%
## 3 USDGBP 1147 1216 94.33%
## 4 USDCHF 862 1215 70.95%
## 5 USDCAD 1134 1214 93.41%
## 6 USDCNY 1184 1215 97.45%
## 7 USDJPY 1191 1215 98.02%
##
## ================ 89.25% ================
##
## Current Tokyo Time : 2018-08-25 23:27:37
## ^fGARCH.APARCH.
##
## .id x n progress
## 1 USDAUD 320 1215 26.34%
## 2 USDEUR 132 1215 10.86%
## 3 USDGBP 320 1216 26.32%
## 4 USDCHF 320 1215 26.34%
## 5 USDCAD 317 1214 26.11%
## 6 USDCNY 317 1215 26.09%
## 7 USDJPY 135 1215 11.11%
##
## ================ 21.88% ================
##
## Current Tokyo Time : 2018-08-25 23:27:38
## ^fGARCH.GJRGARCH.
##
## .id x n progress
## 1 USDAUD 855 1215 70.37%
## 2 USDEUR 1167 1215 96.05%
## 3 USDGBP 1209 1216 99.42%
## 4 USDCHF 1176 1215 96.79%
## 5 USDCAD 1193 1214 98.27%
## 6 USDCNY 918 1215 75.56%
## 7 USDJPY 1203 1215 99.01%
##
## ================ 90.78% ================
##
## Current Tokyo Time : 2018-08-25 23:27:39
## ^fGARCH.ALLGARCH.
##
## .id x n progress
## 1 USDAUD 183 1215 15.06%
## 2 USDEUR 341 1215 28.07%
## 3 USDGBP 340 1216 27.96%
## 4 USDCHF 340 1215 27.98%
## 5 USDCAD 339 1214 27.92%
## 6 USDCNY 341 1215 28.07%
## 7 USDJPY 294 1215 24.20%
##
## ================ 25.61% ================
##
## Current Tokyo Time : 2018-08-25 23:27:40
## ^eGARCH.
##
## .id x n progress
## 1 USDAUD 536 1215 44.12%
## 2 USDEUR 535 1215 44.03%
## 3 USDGBP 537 1216 44.16%
## 4 USDCHF 536 1215 44.12%
## 5 USDCAD 537 1214 44.23%
## 6 USDCNY 535 1215 44.03%
## 7 USDJPY 536 1215 44.12%
##
## ================ 44.12% ================
##
## Current Tokyo Time : 2018-08-25 23:27:41
## ^pred2.
##
## .id x n progress
## 1 USDAUD 1215 1215 100.00%
## 2 USDEUR 1215 1215 100.00%
## 3 USDGBP 1216 1216 100.00%
## 4 USDCHF 1215 1215 100.00%
## 5 USDCAD 1214 1214 100.00%
## 6 USDCNY 1212 1215 99.75%
## 7 USDJPY 1215 1215 100.00%
##
## ================ 99.96% ================
##
## Current Tokyo Time : 2018-08-25 23:27:42
## ^apARCH.
##
## .id x n progress
## 1 USDAUD 116 1215 9.55%
## 2 USDEUR 116 1215 9.55%
## 3 USDGBP 116 1216 9.54%
## 4 USDCHF 115 1215 9.47%
## 5 USDCAD 115 1214 9.47%
## 6 USDCNY 116 1215 9.55%
## 7 USDJPY 113 1215 9.30%
##
## ================ 9.49% ================
##
## Current Tokyo Time : 2018-08-25 23:27:43
## ^iGARCH.
##
## .id x n progress
## 1 USDAUD 1215 1215 100.00%
## 2 USDEUR 1215 1215 100.00%
## 3 USDGBP 1216 1216 100.00%
## 4 USDCHF 1215 1215 100.00%
## 5 USDCAD 1214 1214 100.00%
## 6 USDCNY 1215 1215 100.00%
## 7 USDJPY 1215 1215 100.00%
##
## ================ 100.00% ================
##
## Current Tokyo Time : 2018-08-25 23:27:44
## ^csGARCH.
##
## .id x n progress
## 1 USDAUD 1210 1215 99.59%
## 2 USDEUR 1215 1215 100.00%
## 3 USDGBP 1216 1216 100.00%
## 4 USDCHF 1214 1215 99.92%
## 5 USDCAD 1210 1214 99.67%
## 6 USDCNY 1215 1215 100.00%
## 7 USDJPY 1215 1215 100.00%
##
## ================ 99.88% ================
## check latest date saved in progress.
#' @ l_ply(gmds, function(x) {
#' @ x2 <- ifelse(x == 'gjrGARCH', 'pred2', x)
#' @ task_progress(.date = TRUE, .pattern = paste0('^', x2, '.'), .loops = FALSE)
#' @ })
if (!exists('fx')) {
fx <- read_umodels(cr_code, gmds, mbase, .print = FALSE)
}
acc <- ddply(fx, .(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
acc %>% arrange(.id) %>%
kable(caption = 'Group Table Summary') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
group_rows('USD/AUD', 1, 14, label_row_css = 'background-color: #003399; color: #fff;') %>%
group_rows('USD/CAD', 15, 28, label_row_css = 'background-color: #003399; color: #fff;') %>%
group_rows('USD/CHF', 29, 42, label_row_css = 'background-color: #003399; color: #fff;') %>%
group_rows('USD/CNY', 43, 56, label_row_css = 'background-color: #003399; color: #fff;') %>%
group_rows('USD/EUR', 57, 70, label_row_css = 'background-color: #003399; color: #fff;') %>%
group_rows('USD/GBP', 71, 84, label_row_css = 'background-color: #003399; color: #fff;') %>%
group_rows('USD/JPY', 85, 98, label_row_css = 'background-color: #003399; color: #fff;') %>%
scroll_box(width = '100%', height = '400px')
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 5.000000e-07 | 4857 | 1.647100e-03 | 2.694948e-01 | -7.102248 | -7.022686 | -7.103259 | -7.070268 |
| USDAUD | fGARCH.GARCH | 5.000000e-07 | 4856 | 1.647400e-03 | 2.690199e-01 | -7.101370 | -7.021819 | -7.102379 | -7.069394 |
| USDAUD | fGARCH.TGARCH | 1.159071e+00 | 4812 | 1.180800e-03 | 7.703073e-01 | -6.905361 | -6.812168 | -6.906724 | -6.867902 |
| USDAUD | fGARCH.AVGARCH | 7.432400e+91 | 312 | -4.764359e+89 | 2.671358e+02 | -6.449270 | -6.340982 | -6.451100 | -6.405742 |
| USDAUD | fGARCH.NGARCH | 3.314910e+74 | 4796 | -1.382365e+71 | 4.673981e+03 | -15.440919 | -15.347695 | -15.442283 | -15.403447 |
| USDAUD | fGARCH.NAGARCH | 2.209303e+60 | 4192 | -1.054057e+57 | 2.606909e+01 | -7.062614 | -6.968379 | -7.064007 | -7.024736 |
| USDAUD | fGARCH.APARCH | 2.900000e-06 | 1280 | 6.250000e-03 | 3.641107e+03 | -13.831688 | -13.724372 | -13.833476 | -13.788550 |
| USDAUD | fGARCH.GJRGARCH | 6.000000e-07 | 3420 | 2.339200e-03 | 2.489345e-01 | -7.278103 | -7.185104 | -7.279462 | -7.240721 |
| USDAUD | fGARCH.ALLGARCH | 1.600000e-06 | 736 | 1.086960e-02 | 4.119026e+03 | -15.391667 | -15.265715 | -15.394114 | -15.341038 |
| USDAUD | eGARCH | 5.000000e-07 | 2132 | 3.752300e-03 | 3.331970e+00 | -7.486841 | -7.392624 | -7.488240 | -7.448968 |
| USDAUD | gjrGARCH | 9.000000e-07 | 4860 | 1.646100e-03 | 2.806975e-01 | -7.105727 | -7.012506 | -7.107091 | -7.068257 |
| USDAUD | apARCH | 5.863550e+146 | 464 | -2.527392e+144 | 2.960424e+02 | -7.030944 | -6.918290 | -7.032931 | -6.985660 |
| USDAUD | iGARCH | 1.098765e+287 | 4860 | -4.521666e+283 | 1.146959e+02 | -6.951070 | -6.885141 | -6.951781 | -6.924570 |
| USDAUD | csGARCH | 7.000000e-07 | 4840 | 1.652900e-03 | 2.711930e-01 | -7.087811 | -6.980909 | -7.089582 | -7.044841 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 4.000000e-07 | 4860 | 1.646100e-03 | 3.379221e-01 | -8.119430 | -8.037839 | -8.120496 | -8.086634 |
| USDEUR | fGARCH.GARCH | 1.483144e+181 | 4856 | -6.108501e+177 | 6.410805e+01 | -7.956977 | -7.875412 | -7.958043 | -7.924192 |
| USDEUR | fGARCH.TGARCH | 8.000000e-07 | 4548 | 1.759000e-03 | 5.054985e-01 | -7.979369 | -7.883811 | -7.980805 | -7.940959 |
| USDEUR | fGARCH.AVGARCH | 1.000000e-07 | 180 | 4.444440e-02 | 9.730104e+00 | -7.722639 | -7.616830 | -7.724373 | -7.680108 |
| USDEUR | fGARCH.NGARCH | 8.468312e+98 | 4812 | -3.519664e+95 | 5.364391e+03 | -16.979831 | -16.884791 | -16.981252 | -16.941629 |
| USDEUR | fGARCH.NAGARCH | 4.000000e-07 | 4100 | 1.951200e-03 | 1.695563e+01 | -8.118368 | -8.022222 | -8.119824 | -8.079722 |
| USDEUR | fGARCH.APARCH | 1.000000e-07 | 528 | 1.515150e-02 | 9.174502e+02 | -10.384441 | -10.279031 | -10.386163 | -10.342069 |
| USDEUR | fGARCH.GJRGARCH | 3.000000e-07 | 4668 | 1.713800e-03 | 3.432437e-01 | -8.136069 | -8.040670 | -8.137500 | -8.097723 |
| USDEUR | fGARCH.ALLGARCH | 1.000000e-07 | 1368 | 5.848000e-03 | 2.534296e+02 | -8.755471 | -8.634608 | -8.757709 | -8.706887 |
| USDEUR | eGARCH | 4.000000e-07 | 2140 | 3.738300e-03 | 7.195703e-01 | -8.568110 | -8.471356 | -8.569584 | -8.529218 |
| USDEUR | gjrGARCH | 3.000000e-07 | 4860 | 1.646100e-03 | 3.459734e-01 | -8.136542 | -8.041304 | -8.137969 | -8.098261 |
| USDEUR | apARCH | 1.000000e-07 | 464 | 1.724140e-02 | 3.996040e-02 | -8.169458 | -8.063937 | -8.171186 | -8.127042 |
| USDEUR | iGARCH | 5.000000e-07 | 4860 | 1.646100e-03 | 3.405014e-01 | -8.112925 | -8.044980 | -8.113684 | -8.085614 |
| USDEUR | csGARCH | 2.300000e-06 | 4860 | 1.646100e-03 | 3.318425e-01 | -8.103875 | -7.994992 | -8.105716 | -8.060109 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 7.000000e-07 | 4864 | 1.644700e-03 | 4.306269e-01 | -8.645250 | -8.561637 | -8.646384 | -8.611643 |
| USDGBP | fGARCH.GARCH | 7.000000e-07 | 4860 | 1.646100e-03 | 4.304506e-01 | -8.644493 | -8.560908 | -8.645626 | -8.610897 |
| USDGBP | fGARCH.TGARCH | 2.502052e+143 | 4800 | -1.042521e+140 | 2.969831e+01 | -8.339996 | -8.242703 | -8.341499 | -8.300891 |
| USDGBP | fGARCH.AVGARCH | 0.000000e+00 | 224 | 3.571430e-02 | 4.781526e+01 | -8.126520 | -8.024918 | -8.128121 | -8.085684 |
| USDGBP | fGARCH.NGARCH | 1.128672e+146 | 4808 | -4.694973e+142 | 3.823053e+03 | -14.688168 | -14.590826 | -14.689673 | -14.649043 |
| USDGBP | fGARCH.NAGARCH | 5.000000e-07 | 4588 | 1.743700e-03 | 6.311911e+01 | -8.336187 | -8.239475 | -8.337673 | -8.297315 |
| USDGBP | fGARCH.APARCH | 1.000000e-07 | 1280 | 6.250000e-03 | 1.051663e+03 | -11.668730 | -11.567417 | -11.670321 | -11.628008 |
| USDGBP | fGARCH.GJRGARCH | 6.000000e-07 | 4836 | 1.654300e-03 | 4.283653e-01 | -8.660125 | -8.562876 | -8.661626 | -8.621037 |
| USDGBP | fGARCH.ALLGARCH | 5.285796e+148 | 1364 | -7.750434e+145 | 1.184103e+03 | -10.810643 | -10.694536 | -10.812718 | -10.763974 |
| USDGBP | eGARCH | 1.000000e-07 | 2136 | 3.745300e-03 | 2.956669e+01 | -8.925846 | -8.830782 | -8.927292 | -8.887634 |
| USDGBP | gjrGARCH | 8.000000e-07 | 4864 | 1.644700e-03 | 4.290970e-01 | -8.670272 | -8.573029 | -8.671773 | -8.631187 |
| USDGBP | apARCH | 1.000000e-07 | 464 | 1.724140e-02 | 5.872390e-02 | -9.102982 | -9.000451 | -9.104617 | -9.061773 |
| USDGBP | iGARCH | 9.000000e-07 | 4864 | 1.644700e-03 | 4.297069e-01 | -8.645209 | -8.575227 | -8.646028 | -8.617081 |
| USDGBP | csGARCH | 1.772474e+296 | 4864 | -7.288131e+292 | 1.215273e+02 | -8.473194 | -8.362320 | -8.475116 | -8.428630 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 2.630000e-05 | 4856 | 1.647400e-03 | 3.242167e-01 | -7.629761 | -7.549492 | -7.630794 | -7.597497 |
| USDCHF | fGARCH.GARCH | 2.497679e+121 | 4860 | -1.027851e+118 | 2.905288e+01 | -7.552617 | -7.472346 | -7.553649 | -7.520351 |
| USDCHF | fGARCH.TGARCH | 2.500000e-05 | 4704 | 1.700700e-03 | 4.234093e-01 | -7.552770 | -7.458658 | -7.554164 | -7.514941 |
| USDCHF | fGARCH.AVGARCH | 3.000000e-07 | 76 | 1.052631e-01 | 7.608750e-02 | -7.769682 | -7.656999 | -7.771688 | -7.724381 |
| USDCHF | fGARCH.NGARCH | 1.739084e+00 | 4816 | 9.389000e-04 | 3.906326e+03 | -14.771382 | -14.677354 | -14.772773 | -14.733587 |
| USDCHF | fGARCH.NAGARCH | 6.908758e+287 | 3448 | -4.007400e+284 | 4.414594e+02 | -6.528485 | -6.434230 | -6.529883 | -6.490598 |
| USDCHF | fGARCH.APARCH | 2.500000e-06 | 1280 | 6.250000e-03 | 4.323314e+03 | -15.881751 | -15.773912 | -15.883558 | -15.838401 |
| USDCHF | fGARCH.GJRGARCH | 2.610000e-05 | 4704 | 1.700700e-03 | 3.043563e-01 | -7.650429 | -7.556385 | -7.651821 | -7.612627 |
| USDCHF | fGARCH.ALLGARCH | 1.443016e+13 | 1364 | -2.115860e+10 | 5.594856e+03 | -17.066855 | -16.945434 | -17.069121 | -17.018045 |
| USDCHF | eGARCH | 2.132009e+197 | 2132 | -2.000008e+194 | 1.058906e+01 | -7.878067 | -7.781516 | -7.879542 | -7.839256 |
| USDCHF | gjrGARCH | 4.460000e-05 | 4860 | 1.646100e-03 | 3.123489e-01 | -7.669332 | -7.575414 | -7.670720 | -7.631581 |
| USDCHF | apARCH | 1.000000e-07 | 460 | 1.739130e-02 | 1.387910e-02 | -7.906894 | -7.803521 | -7.908550 | -7.865339 |
| USDCHF | iGARCH | 1.620000e-04 | 4860 | 1.646000e-03 | 4.215382e-01 | -7.576818 | -7.510194 | -7.577548 | -7.550038 |
| USDCHF | csGARCH | 6.450000e-05 | 4856 | 1.647400e-03 | 3.372855e-01 | -7.604900 | -7.497336 | -7.606697 | -7.561664 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 9.000000e-07 | 4856 | 1.647400e-03 | 3.553528e-01 | -7.708202 | -7.626037 | -7.709294 | -7.675175 |
| USDCAD | fGARCH.GARCH | 9.000000e-07 | 4856 | 1.647400e-03 | 3.554005e-01 | -7.708185 | -7.626020 | -7.709277 | -7.675158 |
| USDCAD | fGARCH.TGARCH | 1.900000e-06 | 4724 | 1.693500e-03 | 7.176105e-01 | -7.492619 | -7.396743 | -7.494076 | -7.454081 |
| USDCAD | fGARCH.AVGARCH | 1.000000e-07 | 248 | 3.225810e-02 | 3.687486e+01 | -7.860242 | -7.752867 | -7.862029 | -7.817081 |
| USDCAD | fGARCH.NGARCH | 3.660467e+119 | 4784 | -1.530295e+116 | 5.745730e+03 | -18.389890 | -18.293989 | -18.391348 | -18.351342 |
| USDCAD | fGARCH.NAGARCH | 4.000000e-07 | 4536 | 1.763700e-03 | 2.932958e+00 | -7.726134 | -7.630444 | -7.727585 | -7.687671 |
| USDCAD | fGARCH.APARCH | 5.000000e-07 | 1268 | 6.309100e-03 | 3.744745e+03 | -15.596693 | -15.491530 | -15.598406 | -15.554419 |
| USDCAD | fGARCH.GJRGARCH | 1.000000e-06 | 4772 | 1.676400e-03 | 3.604163e-01 | -7.716214 | -7.620373 | -7.717670 | -7.677690 |
| USDCAD | fGARCH.ALLGARCH | 2.000000e-07 | 1360 | 5.882400e-03 | 4.568140e+03 | -17.164319 | -17.045039 | -17.166501 | -17.116371 |
| USDCAD | eGARCH | 1.000000e-07 | 2132 | 3.752300e-03 | 4.159605e-01 | -8.261885 | -8.169196 | -8.263232 | -8.224627 |
| USDCAD | gjrGARCH | 1.400000e-06 | 4856 | 1.647400e-03 | 3.623402e-01 | -7.712466 | -7.616652 | -7.713921 | -7.673953 |
| USDCAD | apARCH | 0.000000e+00 | 460 | 1.739130e-02 | 9.030400e-03 | -8.376262 | -8.268991 | -8.378048 | -8.333142 |
| USDCAD | iGARCH | 7.000000e-07 | 4856 | 1.647400e-03 | 3.569074e-01 | -7.707116 | -7.638600 | -7.707898 | -7.679575 |
| USDCAD | csGARCH | 5.000000e-07 | 4840 | 1.652900e-03 | 3.543181e-01 | -7.693255 | -7.583768 | -7.695127 | -7.649246 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 5.273000e-04 | 4856 | 1.647200e-03 | 1.197338e+00 | -6.151748 | -6.063258 | -6.152983 | -6.116180 |
| USDCNY | fGARCH.GARCH | 4.171000e-04 | 4856 | 1.647300e-03 | 1.197976e+00 | -6.151725 | -6.063230 | -6.152961 | -6.116155 |
| USDCNY | fGARCH.TGARCH | 6.276028e+03 | 4780 | -2.624280e+00 | 6.332603e+00 | -5.853054 | -5.750984 | -5.854675 | -5.812028 |
| USDCNY | fGARCH.AVGARCH | 1.100000e-06 | 52 | 1.538461e-01 | 2.449294e-01 | -6.841904 | -6.724169 | -6.844013 | -6.794586 |
| USDCNY | fGARCH.NGARCH | 5.652806e+84 | 4812 | -2.349462e+81 | 5.901122e+03 | -17.598434 | -17.496420 | -17.600053 | -17.557430 |
| USDCNY | fGARCH.NAGARCH | 1.821397e+02 | 4736 | -7.522790e-02 | 2.567161e+01 | -5.932229 | -5.830031 | -5.933854 | -5.891151 |
| USDCNY | fGARCH.APARCH | 5.897195e+134 | 1268 | -9.301569e+131 | 1.560942e+04 | -32.887392 | -32.765556 | -32.889652 | -32.838420 |
| USDCNY | fGARCH.GJRGARCH | 4.742892e-01 | 3672 | 1.920300e-03 | 6.907089e+00 | -6.377420 | -6.274790 | -6.379057 | -6.336168 |
| USDCNY | fGARCH.ALLGARCH | 2.514480e+57 | 1364 | -3.686920e+54 | 2.674952e+03 | -11.405354 | -11.268757 | -11.408177 | -11.350449 |
| USDCNY | eGARCH | 7.172000e-04 | 2124 | 3.765800e-03 | 1.649403e+00 | -6.437526 | -6.330912 | -6.439291 | -6.394672 |
| USDCNY | gjrGARCH | 4.138000e-04 | 4848 | 1.650000e-03 | 1.246110e+00 | -6.191716 | -6.089568 | -6.193339 | -6.150658 |
| USDCNY | apARCH | 1.840000e-05 | 464 | 1.724130e-02 | 3.880183e+03 | -9.693012 | -9.574160 | -9.695172 | -9.645243 |
| USDCNY | iGARCH | 6.520000e-04 | 4860 | 1.645800e-03 | 1.329561e+00 | -6.084940 | -6.010098 | -6.085841 | -6.054858 |
| USDCNY | csGARCH | 4.628831e+295 | 4860 | -1.904869e+292 | 1.225855e+02 | -5.967233 | -5.851474 | -5.969295 | -5.920704 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 9.224400e-03 | 4860 | 1.642300e-03 | 2.221979e-01 | 1.813514 | 1.898669 | 1.812339 | 1.847742 |
| USDJPY | fGARCH.GARCH | 9.306400e-03 | 4860 | 1.642300e-03 | 2.216443e-01 | 1.813549 | 1.898705 | 1.812375 | 1.847777 |
| USDJPY | fGARCH.TGARCH | 5.605500e+175 | 4852 | -2.310594e+172 | 3.867787e+01 | 1.910811 | 2.009578 | 1.909263 | 1.950510 |
| USDJPY | fGARCH.AVGARCH | 7.955620e-02 | 244 | 3.213480e-02 | 3.566636e-01 | 1.116023 | 1.253730 | 1.113095 | 1.171370 |
| USDJPY | fGARCH.NGARCH | 3.467923e+245 | 4792 | -1.447380e+242 | 5.001953e+03 | -7.416667 | -7.317867 | -7.418216 | -7.376955 |
| USDJPY | fGARCH.NAGARCH | 6.985600e-03 | 4764 | 1.676300e-03 | 2.288033e-01 | 1.793739 | 1.892446 | 1.792193 | 1.833414 |
| USDJPY | fGARCH.APARCH | 6.514141e+123 | 540 | -2.412645e+121 | 1.703558e+04 | -29.798751 | -29.669021 | -29.801377 | -29.746609 |
| USDJPY | fGARCH.GJRGARCH | 7.894200e-03 | 4812 | 1.659200e-03 | 2.252854e-01 | 1.805879 | 1.904749 | 1.804328 | 1.845620 |
| USDJPY | fGARCH.ALLGARCH | 1.136782e+274 | 1176 | -1.933303e+271 | 7.405377e+03 | -11.224195 | -11.092402 | -11.226886 | -11.171221 |
| USDJPY | eGARCH | 7.335859e+156 | 2128 | -6.894605e+153 | 8.811739e+01 | 2.144005 | 2.249104 | 2.142244 | 2.186250 |
| USDJPY | gjrGARCH | 7.529600e-03 | 4860 | 1.643000e-03 | 2.303997e-01 | 1.802256 | 1.901051 | 1.800708 | 1.841966 |
| USDJPY | apARCH | 3.470295e+242 | 452 | -1.535529e+240 | 1.269101e+05 | -94.407846 | -94.274507 | -94.410609 | -94.354254 |
| USDJPY | iGARCH | 9.308000e-03 | 4860 | 1.642300e-03 | 2.265083e-01 | 1.815783 | 1.887300 | 1.814929 | 1.844529 |
| USDJPY | csGARCH | 6.170350e-02 | 4860 | 1.620700e-03 | 2.221000e-01 | 1.823600 | 1.936033 | 1.821624 | 1.868792 |
acc <- ddply(fx, .(Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
acc %>%
kable(caption = 'Model Summary') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 1.397600e-03 | 34009 | 2.351000e-04 | 11.73935 | -6.220321 | -6.137343 | -6.221427 | -6.186968 |
| fGARCH.GARCH | 2.118029e+180 | 34004 | -1.245753e+176 | 24.83641 | -6.185483 | -6.102513 | -6.186589 | -6.152133 |
| fGARCH.TGARCH | 8.187202e+174 | 33220 | -4.929080e+170 | 22.44225 | -5.995799 | -5.899087 | -5.997274 | -5.956926 |
| fGARCH.AVGARCH | 1.735710e+91 | 1336 | -2.598368e+88 | 89.92217 | -5.872674 | -5.760020 | -5.874667 | -5.827393 |
| fGARCH.NGARCH | 4.942976e+244 | 33620 | -2.940497e+240 | 4927.44149 | -15.042322 | -14.945700 | -15.043794 | -15.003485 |
| fGARCH.NAGARCH | 7.845276e+286 | 30364 | -5.167485e+282 | 81.61159 | -5.870236 | -5.773205 | -5.871720 | -5.831234 |
| fGARCH.APARCH | 1.004520e+134 | 7444 | -2.698870e+130 | 6211.47140 | -18.272610 | -18.162639 | -18.274491 | -18.228405 |
| fGARCH.GJRGARCH | 5.762570e-02 | 30884 | 2.553000e-04 | 13.41298 | -6.226137 | -6.129452 | -6.227613 | -6.187275 |
| fGARCH.ALLGARCH | 1.530984e+273 | 8732 | -3.506606e+269 | 3582.63150 | -12.990230 | -12.865911 | -12.992608 | -12.940258 |
| eGARCH | 3.045726e+196 | 14924 | -4.081649e+192 | 32.14640 | -6.491862 | -6.393729 | -6.493385 | -6.452416 |
| gjrGARCH | 1.141900e-03 | 34008 | 2.352000e-04 | 11.76857 | -6.240673 | -6.144049 | -6.242145 | -6.201835 |
| apARCH | 4.859272e+241 | 3228 | -3.010702e+238 | 19262.68075 | -20.426557 | -20.314686 | -20.428514 | -20.381590 |
| iGARCH | 1.569664e+286 | 34020 | -9.227889e+281 | 28.06237 | -6.180438 | -6.111102 | -6.181232 | -6.152568 |
| csGARCH | 3.199212e+295 | 33980 | -1.882997e+291 | 46.32877 | -6.156747 | -6.046472 | -6.158638 | -6.112422 |
Here I put this section as next topic as Markov Method 2 : Filtered MSE due to I need to filter OHLC, Close and HiLo three sub-sections.
Due to some errors, the MSE values is not accurate. I can either filter AIC and BIC values or MSE values. Since the standard deviation based on price, even though the AIC value does not bias, but finally we take price figure but not the AIC figure.
There is the solution for filter unknown error. Here I filtered all dataset which \(\sigma^2_{i} >= 0.2\) and the AIC, BIC values just for reference in order to know there has .
## filter all predictive error.
#'@ fx %>% mutate(diff = Price.T1 - Price, se = ifelse(abs(diff) > Price, 1, 0)) %>% .[,-c(8:10)] %>% dplyr::filter(se == 1) %>% data.frame
fx %<>% mutate(diff = abs(Price.T1/Price),
se = ifelse(diff <= 0.8 | diff >= 1.25, 1, 0))
## filter all predictive error where sd >= 20%.
notID <- fx %>% dplyr::filter(se == 1)
ntimeID <- notID %>% .$Date %>% unique
## filter all date which contain OHLC of 7 currencies.
ntimeID2 <- fx %>% dplyr::count(Date) %>%
dplyr::filter(n == 392) %>% .$Date #14 models x 7 currencies x OHLC 4 types = 392 observations per day.
acc <- fx %>%
dplyr::filter(!Date %in% ntimeID) %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 0.0000005 | 4353 | 0.0018378 | 2.639467e-01 | -7.054219 | -6.975317 | -7.055209 | -7.022504 |
| USDAUD | fGARCH.GARCH | 0.0000005 | 4352 | 0.0018382 | 2.633802e-01 | -7.053272 | -6.974384 | -7.054261 | -7.021562 |
| USDAUD | fGARCH.TGARCH | 0.0000026 | 4312 | 0.0018553 | 5.399479e-01 | -6.865302 | -6.772757 | -6.866642 | -6.828103 |
| USDAUD | fGARCH.AVGARCH | 0.0000001 | 264 | 0.0303030 | 3.855170e+01 | -7.236056 | -7.128579 | -7.237854 | -7.192854 |
| USDAUD | fGARCH.NGARCH | 0.0000038 | 4292 | 0.0018639 | 4.353914e+03 | -14.941662 | -14.849108 | -14.943003 | -14.904460 |
| USDAUD | fGARCH.NAGARCH | 0.0000011 | 3700 | 0.0021622 | 1.628331e+01 | -7.099948 | -7.006363 | -7.101318 | -7.062331 |
| USDAUD | fGARCH.APARCH | 0.0000019 | 1116 | 0.0071685 | 2.981676e+03 | -12.669296 | -12.562917 | -12.671049 | -12.626534 |
| USDAUD | fGARCH.GJRGARCH | 0.0000006 | 2936 | 0.0027248 | 2.585403e-01 | -7.232835 | -7.140805 | -7.234162 | -7.195843 |
| USDAUD | fGARCH.ALLGARCH | 0.0000018 | 600 | 0.0133333 | 3.147065e+03 | -13.596206 | -13.471355 | -13.598607 | -13.546020 |
| USDAUD | eGARCH | 0.0000006 | 1728 | 0.0046296 | 4.086942e+00 | -7.459670 | -7.366463 | -7.461033 | -7.422203 |
| USDAUD | gjrGARCH | 0.0000010 | 4356 | 0.0018365 | 2.750966e-01 | -7.057120 | -6.964559 | -7.058461 | -7.019915 |
| USDAUD | apARCH | 0.0000004 | 380 | 0.0210526 | 1.157250e-02 | -7.821905 | -7.710452 | -7.823847 | -7.777104 |
| USDAUD | iGARCH | 0.0000006 | 4356 | 0.0018365 | 2.649267e-01 | -7.056601 | -6.991330 | -7.057295 | -7.030365 |
| USDAUD | csGARCH | 0.0000007 | 4336 | 0.0018450 | 2.658534e-01 | -7.039799 | -6.933557 | -7.041544 | -6.997095 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 0.0000004 | 4356 | 0.0018365 | 3.063516e-01 | -8.057918 | -7.976608 | -8.058976 | -8.025235 |
| USDEUR | fGARCH.GARCH | 0.0000004 | 4356 | 0.0018365 | 3.063353e-01 | -8.057905 | -7.976596 | -8.058964 | -8.025223 |
| USDEUR | fGARCH.TGARCH | 0.0000007 | 4072 | 0.0019646 | 4.720089e-01 | -7.912641 | -7.817375 | -7.914068 | -7.874349 |
| USDEUR | fGARCH.AVGARCH | 0.0000001 | 156 | 0.0512820 | 1.115540e+01 | -7.694693 | -7.588904 | -7.696424 | -7.652170 |
| USDEUR | fGARCH.NGARCH | 0.0000017 | 4308 | 0.0018570 | 5.221469e+03 | -16.666911 | -16.572179 | -16.668322 | -16.628833 |
| USDEUR | fGARCH.NAGARCH | 0.0000004 | 3604 | 0.0022198 | 1.920156e+01 | -8.043237 | -7.947295 | -8.044685 | -8.004672 |
| USDEUR | fGARCH.APARCH | 0.0000001 | 424 | 0.0188679 | 7.531245e+02 | -9.633356 | -9.527642 | -9.635090 | -9.590862 |
| USDEUR | fGARCH.GJRGARCH | 0.0000003 | 4172 | 0.0019175 | 3.123974e-01 | -8.074067 | -7.978962 | -8.075489 | -8.035839 |
| USDEUR | fGARCH.ALLGARCH | 0.0000001 | 1192 | 0.0067114 | 2.908084e+02 | -8.822347 | -8.701288 | -8.824592 | -8.773684 |
| USDEUR | eGARCH | 0.0000002 | 1740 | 0.0045977 | 8.266600e-01 | -8.525797 | -8.428926 | -8.527274 | -8.486858 |
| USDEUR | gjrGARCH | 0.0000003 | 4356 | 0.0018365 | 3.160686e-01 | -8.075367 | -7.980413 | -8.076785 | -8.037200 |
| USDEUR | apARCH | 0.0000001 | 380 | 0.0210526 | 4.500760e-02 | -8.162310 | -8.056438 | -8.164050 | -8.119753 |
| USDEUR | iGARCH | 0.0000004 | 4356 | 0.0018365 | 3.089101e-01 | -8.051340 | -7.983675 | -8.052092 | -8.024142 |
| USDEUR | csGARCH | 0.0000024 | 4356 | 0.0018365 | 3.012516e-01 | -8.043247 | -7.934647 | -8.045078 | -7.999595 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 0.0000007 | 4360 | 0.0018349 | 4.201150e-01 | -8.581922 | -8.498431 | -8.583050 | -8.548364 |
| USDGBP | fGARCH.GARCH | 0.0000008 | 4356 | 0.0018365 | 4.198945e-01 | -8.581300 | -8.497838 | -8.582427 | -8.547754 |
| USDGBP | fGARCH.TGARCH | 0.0000008 | 4312 | 0.0018553 | 6.616308e-01 | -8.360653 | -8.263507 | -8.362149 | -8.321607 |
| USDGBP | fGARCH.AVGARCH | 0.0000000 | 180 | 0.0444444 | 5.930195e+01 | -7.949880 | -7.847750 | -7.951499 | -7.908832 |
| USDGBP | fGARCH.NGARCH | 0.0000016 | 4304 | 0.0018587 | 3.683537e+03 | -14.369131 | -14.271901 | -14.370630 | -14.330051 |
| USDGBP | fGARCH.NAGARCH | 0.0000005 | 4092 | 0.0019550 | 5.540591e+01 | -8.293999 | -8.197469 | -8.295476 | -8.255200 |
| USDGBP | fGARCH.APARCH | 0.0000001 | 1116 | 0.0071685 | 1.201960e+03 | -12.150823 | -12.049240 | -12.152424 | -12.109992 |
| USDGBP | fGARCH.GJRGARCH | 0.0000007 | 4332 | 0.0018467 | 4.178588e-01 | -8.596547 | -8.499421 | -8.598042 | -8.557509 |
| USDGBP | fGARCH.ALLGARCH | 0.0000001 | 1188 | 0.0067340 | 9.051736e+02 | -10.743311 | -10.627055 | -10.745391 | -10.696582 |
| USDGBP | eGARCH | 0.0000001 | 1728 | 0.0046296 | 4.495302e+00 | -9.002430 | -8.907963 | -9.003857 | -8.964459 |
| USDGBP | gjrGARCH | 0.0000009 | 4360 | 0.0018349 | 4.178604e-01 | -8.607545 | -8.510425 | -8.609040 | -8.568509 |
| USDGBP | apARCH | 0.0000001 | 380 | 0.0210526 | 6.977770e-02 | -9.096750 | -8.993677 | -9.098404 | -9.055323 |
| USDGBP | iGARCH | 0.0000009 | 4360 | 0.0018349 | 4.193792e-01 | -8.582230 | -8.512368 | -8.583044 | -8.554150 |
| USDGBP | csGARCH | 0.0000009 | 4360 | 0.0018349 | 4.091090e-01 | -8.568685 | -8.457936 | -8.570601 | -8.524172 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 0.0000027 | 4352 | 0.0018382 | 3.074894e-01 | -7.597091 | -7.517044 | -7.598115 | -7.564916 |
| USDCHF | fGARCH.GARCH | 0.0000027 | 4356 | 0.0018365 | 3.076617e-01 | -7.596998 | -7.516949 | -7.598022 | -7.564822 |
| USDCHF | fGARCH.TGARCH | 0.0000017 | 4224 | 0.0018939 | 4.079930e-01 | -7.516464 | -7.422573 | -7.517849 | -7.478724 |
| USDCHF | fGARCH.AVGARCH | 0.0000004 | 72 | 0.1111111 | 6.717750e-02 | -7.785479 | -7.671861 | -7.787518 | -7.739802 |
| USDCHF | fGARCH.NGARCH | 0.0000022 | 4312 | 0.0018553 | 3.741176e+03 | -14.212570 | -14.118755 | -14.213952 | -14.174860 |
| USDCHF | fGARCH.NAGARCH | 0.0000022 | 2996 | 0.0026702 | 1.053977e+02 | -7.001939 | -6.907812 | -7.003330 | -6.964104 |
| USDCHF | fGARCH.APARCH | 0.0000026 | 1116 | 0.0071685 | 4.129926e+03 | -15.560998 | -15.452808 | -15.562817 | -15.517507 |
| USDCHF | fGARCH.GJRGARCH | 0.0000018 | 4200 | 0.0019048 | 2.894848e-01 | -7.615780 | -7.521953 | -7.617163 | -7.578066 |
| USDCHF | fGARCH.ALLGARCH | 0.0000018 | 1192 | 0.0067114 | 5.480405e+03 | -16.681058 | -16.559332 | -16.683336 | -16.632126 |
| USDCHF | eGARCH | 0.0000002 | 1728 | 0.0046296 | 4.216853e-01 | -7.956792 | -7.860186 | -7.958265 | -7.917959 |
| USDCHF | gjrGARCH | 0.0000019 | 4356 | 0.0018365 | 2.899817e-01 | -7.635360 | -7.541665 | -7.636739 | -7.597699 |
| USDCHF | apARCH | 0.0000001 | 376 | 0.0212766 | 1.433500e-02 | -7.904426 | -7.800344 | -7.906108 | -7.862586 |
| USDCHF | iGARCH | 0.0000373 | 4356 | 0.0018365 | 4.063522e-01 | -7.542770 | -7.476368 | -7.543493 | -7.516079 |
| USDCHF | csGARCH | 0.0000115 | 4352 | 0.0018382 | 3.172078e-01 | -7.574225 | -7.466885 | -7.576012 | -7.531079 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 0.0000009 | 4352 | 0.0018382 | 3.484554e-01 | -7.651658 | -7.569697 | -7.652744 | -7.618714 |
| USDCAD | fGARCH.GARCH | 0.0000009 | 4352 | 0.0018382 | 3.486561e-01 | -7.651617 | -7.569655 | -7.652702 | -7.618672 |
| USDCAD | fGARCH.TGARCH | 0.0000020 | 4232 | 0.0018904 | 6.877543e-01 | -7.429481 | -7.333748 | -7.430933 | -7.391001 |
| USDCAD | fGARCH.AVGARCH | 0.0000001 | 208 | 0.0384615 | 4.391638e+01 | -7.780511 | -7.674241 | -7.782256 | -7.737794 |
| USDCAD | fGARCH.NGARCH | 0.0000062 | 4280 | 0.0018692 | 5.744082e+03 | -18.284843 | -18.189140 | -18.286294 | -18.246375 |
| USDCAD | fGARCH.NAGARCH | 0.0000004 | 4040 | 0.0019802 | 3.240929e+00 | -7.667755 | -7.572270 | -7.669198 | -7.629374 |
| USDCAD | fGARCH.APARCH | 0.0000005 | 1108 | 0.0072202 | 3.569546e+03 | -15.325897 | -15.221105 | -15.327596 | -15.283773 |
| USDCAD | fGARCH.GJRGARCH | 0.0000010 | 4268 | 0.0018744 | 3.547396e-01 | -7.659221 | -7.563586 | -7.660669 | -7.620780 |
| USDCAD | fGARCH.ALLGARCH | 0.0000003 | 1184 | 0.0067568 | 4.945529e+03 | -18.018991 | -17.900107 | -18.021156 | -17.971202 |
| USDCAD | eGARCH | 0.0000001 | 1724 | 0.0046404 | 5.026999e-01 | -8.249696 | -8.157482 | -8.251026 | -8.212629 |
| USDCAD | gjrGARCH | 0.0000015 | 4352 | 0.0018382 | 3.538860e-01 | -7.656276 | -7.560666 | -7.657723 | -7.617845 |
| USDCAD | apARCH | 0.0000000 | 376 | 0.0212766 | 9.063000e-03 | -8.368868 | -8.262488 | -8.370620 | -8.326107 |
| USDCAD | iGARCH | 0.0000008 | 4352 | 0.0018382 | 3.503874e-01 | -7.650523 | -7.582210 | -7.651300 | -7.623064 |
| USDCAD | csGARCH | 0.0000005 | 4336 | 0.0018450 | 3.477300e-01 | -7.636842 | -7.527559 | -7.638706 | -7.592915 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 0.0003984 | 4352 | 0.0018381 | 1.088113e+00 | -6.140296 | -6.051506 | -6.141540 | -6.104608 |
| USDCNY | fGARCH.GARCH | 0.0002765 | 4352 | 0.0018381 | 1.088311e+00 | -6.140281 | -6.051484 | -6.141524 | -6.104589 |
| USDCNY | fGARCH.TGARCH | 0.0010889 | 4280 | 0.0018687 | 5.808491e+00 | -5.845388 | -5.743026 | -5.847018 | -5.804244 |
| USDCNY | fGARCH.AVGARCH | 0.0000011 | 52 | 0.1538461 | 2.449294e-01 | -6.841904 | -6.724169 | -6.844013 | -6.794586 |
| USDCNY | fGARCH.NGARCH | 0.0009158 | 4308 | 0.0018566 | 3.447556e+03 | -13.275064 | -13.172761 | -13.276692 | -13.233944 |
| USDCNY | fGARCH.NAGARCH | 0.0001963 | 4236 | 0.0018885 | 1.504602e+01 | -6.003231 | -5.900732 | -6.004865 | -5.962032 |
| USDCNY | fGARCH.APARCH | 0.0006557 | 1104 | 0.0072452 | 1.550051e+04 | -32.302867 | -32.180685 | -32.305139 | -32.253756 |
| USDCNY | fGARCH.GJRGARCH | 0.0003279 | 3180 | 0.0025155 | 1.015691e+00 | -6.455477 | -6.352294 | -6.457132 | -6.414002 |
| USDCNY | fGARCH.ALLGARCH | 0.0000403 | 1188 | 0.0067339 | 2.292978e+03 | -10.691252 | -10.554318 | -10.694088 | -10.636212 |
| USDCNY | eGARCH | 0.0004393 | 1720 | 0.0046507 | 1.419151e+00 | -6.490264 | -6.382305 | -6.492071 | -6.446870 |
| USDCNY | gjrGARCH | 0.0003015 | 4348 | 0.0018398 | 1.149739e+00 | -6.182369 | -6.079934 | -6.184001 | -6.141196 |
| USDCNY | apARCH | 0.0000173 | 380 | 0.0210525 | 4.735451e+03 | -10.358168 | -10.238715 | -10.360350 | -10.310157 |
| USDCNY | iGARCH | 0.0004641 | 4356 | 0.0018363 | 1.237915e+00 | -6.066670 | -5.991528 | -6.067577 | -6.036467 |
| USDCNY | csGARCH | 0.0005762 | 4356 | 0.0018363 | 1.226573e+00 | -6.111496 | -5.995440 | -6.113568 | -6.064848 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 0.0089049 | 4356 | 0.0018325 | 2.049552e-01 | 1.860380 | 1.944878 | 1.859224 | 1.894343 |
| USDJPY | fGARCH.GARCH | 0.0089134 | 4356 | 0.0018325 | 2.044528e-01 | 1.860324 | 1.944822 | 1.859169 | 1.894288 |
| USDJPY | fGARCH.TGARCH | 0.0078400 | 4352 | 0.0018346 | 2.186595e-01 | 1.867765 | 1.965878 | 1.866238 | 1.907201 |
| USDJPY | fGARCH.AVGARCH | 0.0623884 | 204 | 0.0386040 | 3.971346e-01 | 1.096750 | 1.233458 | 1.093865 | 1.151696 |
| USDJPY | fGARCH.NGARCH | 0.0386002 | 4292 | 0.0018459 | 4.467445e+03 | -6.821190 | -6.723022 | -6.822718 | -6.781732 |
| USDJPY | fGARCH.NAGARCH | 0.0064642 | 4260 | 0.0018749 | 2.112853e-01 | 1.841350 | 1.939373 | 1.839826 | 1.880750 |
| USDJPY | fGARCH.APARCH | 93.5534852 | 432 | -0.4145995 | 1.451855e+04 | -25.238090 | -25.108920 | -25.240696 | -25.186174 |
| USDJPY | fGARCH.GJRGARCH | 0.0074342 | 4308 | 0.0018536 | 2.078527e-01 | 1.853041 | 1.951253 | 1.851511 | 1.892516 |
| USDJPY | fGARCH.ALLGARCH | 0.5988183 | 1028 | 0.0066171 | 5.643592e+03 | -8.686667 | -8.555768 | -8.689322 | -8.634053 |
| USDJPY | eGARCH | 0.0184655 | 1724 | 0.0046189 | 9.495368e-01 | 1.718331 | 1.823128 | 1.716580 | 1.760454 |
| USDJPY | gjrGARCH | 0.0070842 | 4356 | 0.0018333 | 2.121519e-01 | 1.849902 | 1.948038 | 1.848375 | 1.889347 |
| USDJPY | apARCH | 0.1023505 | 368 | 0.0211829 | 1.133928e+05 | -87.055020 | -86.922644 | -87.057747 | -87.001815 |
| USDJPY | iGARCH | 0.0088948 | 4356 | 0.0018325 | 2.089536e-01 | 1.863369 | 1.934229 | 1.862531 | 1.891850 |
| USDJPY | csGARCH | 0.0103491 | 4356 | 0.0018318 | 2.042932e-01 | 1.869709 | 1.981483 | 1.867758 | 1.914636 |
6.1.1.1A : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 0.0013302 | 30481 | 0.0002624 | 11.69308 | -6.174528 | -6.091814 | -6.175626 | -6.141281 |
| fGARCH.GARCH | 0.0013141 | 30480 | 0.0002624 | 11.69196 | -6.174131 | -6.091422 | -6.175228 | -6.140886 |
| fGARCH.TGARCH | 0.0013032 | 29784 | 0.0002685 | 12.34034 | -5.974867 | -5.878416 | -5.976333 | -5.936099 |
| fGARCH.AVGARCH | 0.0112037 | 1136 | 0.0070225 | 39.22538 | -6.032229 | -5.919944 | -6.034204 | -5.987096 |
| fGARCH.NGARCH | 0.0056381 | 30096 | 0.0002654 | 4389.78791 | -14.081096 | -13.984737 | -14.082559 | -14.042365 |
| fGARCH.NAGARCH | 0.0010541 | 26928 | 0.0002970 | 39.60966 | -5.894896 | -5.798098 | -5.896372 | -5.855988 |
| fGARCH.APARCH | 6.2992262 | 6416 | -0.0007167 | 5813.32468 | -17.564867 | -17.455071 | -17.566741 | -17.520733 |
| fGARCH.GJRGARCH | 0.0012077 | 27396 | 0.0002919 | 12.79307 | -6.182735 | -6.086327 | -6.184200 | -6.143984 |
| fGARCH.ALLGARCH | 0.0813044 | 7572 | 0.0010350 | 3211.86964 | -12.451984 | -12.327787 | -12.454357 | -12.402061 |
| eGARCH | 0.0026953 | 12092 | 0.0006611 | 13.79592 | -6.570796 | -6.472786 | -6.572314 | -6.531400 |
| gjrGARCH | 0.0010561 | 30484 | 0.0002624 | 11.72395 | -6.195004 | -6.098647 | -6.196467 | -6.156274 |
| apARCH | 0.0142696 | 2640 | 0.0030195 | 17226.59526 | -19.553741 | -19.442002 | -19.555692 | -19.508828 |
| iGARCH | 0.0013427 | 30492 | 0.0002623 | 11.70932 | -6.155374 | -6.086301 | -6.156161 | -6.127610 |
| csGARCH | 0.0015651 | 30452 | 0.0002626 | 11.70696 | -6.156378 | -6.046368 | -6.158259 | -6.112160 |
6.1.1.1B : Table summary
| Model | n |
|---|---|
| sGARCH | 2 |
| fGARCH.GARCH | 5 |
| fGARCH.TGARCH | 5 |
| fGARCH.AVGARCH | 1 |
| fGARCH.NGARCH | 74 |
| fGARCH.NAGARCH | 14 |
| fGARCH.APARCH | 6 |
| fGARCH.GJRGARCH | 4 |
| fGARCH.ALLGARCH | 11 |
| eGARCH | 11 |
| gjrGARCH | 3 |
| apARCH | 10 |
| iGARCH | 10 |
| csGARCH | 5 |
6.1.1.1C : Table summary number of errors.
| .id | Model | Date | Type | Price | Price.T1 | Akaike | Bayes | Shibata | Hannan.Quinn | diff | se |
|---|---|---|---|---|---|---|---|---|---|---|---|
| USDAUD | fGARCH.TGARCH | 2013-06-03 | USDAUD.Op | 1.02600 | -7.365624e+01 | 24.941247 | 25.064162 | 24.938973 | 24.990655 | 7.178971e+01 | 1 |
| USDAUD | fGARCH.AVGARCH | 2013-04-11 | USDAUD.Op | 0.94800 | -1.522796e+47 | 263.587327 | 263.764870 | 263.582672 | 263.658694 | 1.606325e+47 | 1 |
| USDAUD | fGARCH.NGARCH | 2013-06-27 | USDAUD.Lo | 1.07700 | 2.542027e+00 | -590.320340 | -590.197426 | -590.322615 | -590.270933 | 2.360285e+00 | 1 |
| USDAUD | fGARCH.NGARCH | 2013-08-04 | USDAUD.Op | 1.12300 | 1.260885e+39 | -299.194470 | -299.084911 | -299.196290 | -299.150426 | 1.122783e+39 | 1 |
| USDAUD | fGARCH.NGARCH | 2013-08-04 | USDAUD.Cl | 1.12290 | 9.147871e+10 | 192.689015 | 192.798574 | 192.687195 | 192.733059 | 8.146648e+10 | 1 |
| USDAUD | fGARCH.NGARCH | 2014-04-14 | USDAUD.Op | 1.06200 | 1.419924e+09 | -416.149142 | -416.012570 | -416.151936 | -416.094244 | 1.337028e+09 | 1 |
| USDAUD | fGARCH.NGARCH | 2014-07-24 | USDAUD.Hi | 1.06400 | 2.487249e+34 | -502.592743 | -502.428857 | -502.596729 | -502.526867 | 2.337640e+34 | 1 |
| USDAUD | fGARCH.NGARCH | 2017-03-26 | USDAUD.Lo | 1.30700 | 1.111220e-02 | -586.980288 | -586.857373 | -586.982562 | -586.930880 | 8.502100e-03 | 1 |
| USDAUD | fGARCH.NAGARCH | 2015-02-09 | USDAUD.Op | 1.28800 | 9.042209e+09 | 101.921621 | 102.058192 | 101.918826 | 101.976518 | 7.020349e+09 | 1 |
| USDAUD | fGARCH.NAGARCH | 2015-02-10 | USDAUD.Op | 1.28300 | -9.623617e+31 | 153.814604 | 153.950801 | 153.811831 | 153.869344 | 7.500870e+31 | 1 |
| USDAUD | apARCH | 2013-05-16 | USDAUD.Hi | 1.03000 | 5.216021e+74 | 363.188288 | 363.379488 | 363.182914 | 363.265144 | 5.064098e+74 | 1 |
| USDAUD | iGARCH | 2014-10-15 | USDAUD.Cl | 1.13730 | 2.310843e+145 | 738.699064 | 738.808021 | 738.697272 | 738.742856 | 2.031868e+145 | 1 |
| USDEUR | fGARCH.GARCH | 2015-02-05 | USDEUR.Hi | 0.88400 | 2.683682e+92 | 412.262447 | 412.385024 | 412.260190 | 412.311713 | 3.035839e+92 | 1 |
| USDEUR | fGARCH.GARCH | 2017-06-18 | USDEUR.Cl | 0.89220 | 6.667688e+68 | 356.680437 | 356.817009 | 356.677643 | 356.735335 | 7.473311e+68 | 1 |
| USDEUR | fGARCH.NGARCH | 2014-10-14 | USDEUR.Lo | 0.77900 | -2.018651e+51 | -468.909622 | -468.759806 | -468.912961 | -468.849407 | 2.591336e+51 | 1 |
| USDEUR | fGARCH.NGARCH | 2015-03-02 | USDEUR.Lo | 0.89000 | -4.015994e+07 | 83.346290 | 83.510176 | 83.342305 | 83.412167 | 4.512353e+07 | 1 |
| USDEUR | fGARCH.NGARCH | 2015-06-04 | USDEUR.Lo | 0.88700 | -1.394863e+18 | -545.380537 | -545.244340 | -545.383310 | -545.325796 | 1.572562e+18 | 1 |
| USDEUR | fGARCH.NGARCH | 2015-06-24 | USDEUR.Lo | 0.89100 | 1.892803e+10 | 77.586765 | 77.722962 | 77.583992 | 77.641506 | 2.124358e+10 | 1 |
| USDGBP | fGARCH.TGARCH | 2014-06-19 | USDGBP.Lo | 0.58600 | -3.465523e+73 | 364.832355 | 365.037213 | 364.826216 | 364.914701 | 5.913861e+73 | 1 |
| USDGBP | fGARCH.NGARCH | 2014-03-31 | USDGBP.Cl | 0.60001 | -1.642110e+04 | -444.661563 | -444.524991 | -444.664357 | -444.606666 | 2.736805e+04 | 1 |
| USDGBP | fGARCH.NGARCH | 2014-05-01 | USDGBP.Cl | 0.59188 | 9.637298e-01 | -516.051131 | -515.914560 | -516.053925 | -515.996234 | 1.628252e+00 | 1 |
| USDGBP | fGARCH.NGARCH | 2014-06-19 | USDGBP.Lo | 0.58600 | 4.316118e-01 | -160.018385 | -159.813528 | -160.024525 | -159.936039 | 7.365389e-01 | 1 |
| USDGBP | fGARCH.NGARCH | 2015-04-16 | USDGBP.Cl | 0.67016 | 1.865748e+15 | -556.647438 | -556.511242 | -556.650211 | -556.592698 | 2.784033e+15 | 1 |
| USDGBP | fGARCH.NGARCH | 2015-04-21 | USDGBP.Op | 0.67000 | -1.002521e+06 | -574.983967 | -574.847770 | -574.986740 | -574.929227 | 1.496300e+06 | 1 |
| USDGBP | fGARCH.NGARCH | 2015-06-08 | USDGBP.Op | 0.65200 | 5.022905e+36 | -490.210255 | -490.087678 | -490.212512 | -490.160989 | 7.703841e+36 | 1 |
| USDGBP | fGARCH.NGARCH | 2015-06-16 | USDGBP.Op | 0.63900 | 1.392346e+72 | 349.939882 | 350.048839 | 349.938090 | 349.983675 | 2.178945e+72 | 1 |
| USDGBP | fGARCH.NGARCH | 2016-07-19 | USDGBP.Cl | 0.76287 | -6.365327e+09 | 114.898499 | 115.034323 | 114.895747 | 114.953084 | 8.343921e+09 | 1 |
| USDGBP | fGARCH.NGARCH | 2016-07-20 | USDGBP.Hi | 0.75900 | 7.366569e+74 | -405.810489 | -405.701830 | -405.812268 | -405.766822 | 9.705624e+74 | 1 |
| USDGBP | fGARCH.ALLGARCH | 2014-03-17 | USDGBP.Op | 0.60100 | 1.849141e+38 | -496.809119 | -496.644780 | -496.813134 | -496.743052 | 3.076773e+38 | 1 |
| USDGBP | fGARCH.ALLGARCH | 2014-04-06 | USDGBP.Op | 0.60300 | -8.491069e+75 | 422.062223 | 422.240257 | 422.057533 | 422.133795 | 1.408138e+76 | 1 |
| USDGBP | csGARCH | 2014-12-05 | USDGBP.Lo | 0.63700 | 9.285102e+149 | 758.957433 | 759.107249 | 758.954093 | 759.017647 | 1.457630e+150 | 1 |
| USDCHF | sGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.189676e+00 | -6.687989 | -6.606271 | -6.689007 | -6.655145 | 1.399619e+00 | 1 |
| USDCHF | fGARCH.GARCH | 2014-05-25 | USDCHF.Hi | 0.89700 | -3.484066e+62 | 366.067877 | 366.273301 | 366.061692 | 366.150461 | 3.884132e+62 | 1 |
| USDCHF | fGARCH.GARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.189676e+00 | -6.687989 | -6.606271 | -6.689007 | -6.655145 | 1.399619e+00 | 1 |
| USDCHF | fGARCH.TGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.182560e+00 | -6.882116 | -6.786779 | -6.883495 | -6.843798 | 1.391247e+00 | 1 |
| USDCHF | fGARCH.NGARCH | 2013-12-12 | USDCHF.Op | 0.88700 | -3.879205e+00 | -432.539483 | -432.402912 | -432.542277 | -432.484586 | 4.373400e+00 | 1 |
| USDCHF | fGARCH.NGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.182556e+00 | -6.811955 | -6.716617 | -6.813334 | -6.773637 | 1.391243e+00 | 1 |
| USDCHF | fGARCH.NGARCH | 2015-09-07 | USDCHF.Lo | 0.97000 | -8.823318e+01 | -587.029347 | -586.920390 | -587.031140 | -586.985555 | 9.096204e+01 | 1 |
| USDCHF | fGARCH.NGARCH | 2015-10-30 | USDCHF.Hi | 0.99100 | -1.889325e+01 | -584.267632 | -584.158374 | -584.269437 | -584.223714 | 1.906483e+01 | 1 |
| USDCHF | fGARCH.NAGARCH | 2013-12-05 | USDCHF.Op | 0.90200 | 4.359195e+145 | 731.450007 | 731.586578 | 731.447212 | 731.504904 | 4.832810e+145 | 1 |
| USDCHF | fGARCH.NAGARCH | 2013-12-16 | USDCHF.Op | 0.89000 | 2.195181e+145 | 732.215372 | 732.352321 | 732.212557 | 732.270427 | 2.466495e+145 | 1 |
| USDCHF | fGARCH.NAGARCH | 2015-01-09 | USDCHF.Op | 1.01800 | -1.228938e+24 | 226.375920 | 226.539355 | 226.371964 | 226.441608 | 1.207208e+24 | 1 |
| USDCHF | fGARCH.NAGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.188451e+00 | -6.758750 | -6.663413 | -6.760129 | -6.720432 | 1.398178e+00 | 1 |
| USDCHF | fGARCH.GJRGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.189203e+00 | -6.775060 | -6.679723 | -6.776439 | -6.736742 | 1.399062e+00 | 1 |
| USDCHF | fGARCH.ALLGARCH | 2014-03-13 | USDCHF.Op | 0.87400 | 1.402952e+08 | -564.395228 | -564.231341 | -564.399213 | -564.329351 | 1.605208e+08 | 1 |
| USDCHF | eGARCH | 2014-01-13 | USDCHF.Op | 0.90200 | 2.132004e+100 | 108.984490 | 109.121440 | 108.981675 | 109.039546 | 2.363641e+100 | 1 |
| USDCHF | eGARCH | 2014-08-28 | USDCHF.Cl | 0.91504 | -3.241158e+02 | 62.349543 | 62.472457 | 62.347269 | 62.398951 | 3.542094e+02 | 1 |
| USDCHF | eGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.179679e+00 | -6.756294 | -6.660957 | -6.757673 | -6.717976 | 1.387858e+00 | 1 |
| USDCHF | eGARCH | 2015-01-21 | USDCHF.Lo | 0.85100 | 5.746862e-01 | -6.615293 | -6.519955 | -6.616671 | -6.576975 | 6.753070e-01 | 1 |
| USDCHF | gjrGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.187461e+00 | -6.834457 | -6.739119 | -6.835835 | -6.796138 | 1.397013e+00 | 1 |
| USDCHF | gjrGARCH | 2015-01-19 | USDCHF.Lo | 0.85700 | 5.503465e-01 | -6.799206 | -6.703606 | -6.800595 | -6.760778 | 6.421780e-01 | 1 |
| USDCHF | iGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.189656e+00 | -6.696311 | -6.628212 | -6.697021 | -6.668940 | 1.399595e+00 | 1 |
| USDCHF | iGARCH | 2015-01-19 | USDCHF.Lo | 0.85700 | 5.467194e-01 | -6.659730 | -6.591444 | -6.660445 | -6.632281 | 6.379457e-01 | 1 |
| USDCHF | iGARCH | 2015-01-20 | USDCHF.Lo | 0.86900 | 1.169574e+00 | -6.632037 | -6.563939 | -6.632748 | -6.604667 | 1.345885e+00 | 1 |
| USDCHF | iGARCH | 2015-01-21 | USDCHF.Lo | 0.85100 | 5.536845e-01 | -6.599117 | -6.531019 | -6.599827 | -6.571747 | 6.506281e-01 | 1 |
| USDCHF | iGARCH | 2015-01-22 | USDCHF.Lo | 0.85300 | 1.132264e+00 | -6.569994 | -6.501896 | -6.570705 | -6.542624 | 1.327390e+00 | 1 |
| USDCHF | iGARCH | 2015-01-26 | USDCHF.Lo | 0.87600 | 1.153558e+00 | -6.519110 | -6.450824 | -6.519825 | -6.491661 | 1.316847e+00 | 1 |
| USDCHF | iGARCH | 2015-01-27 | USDCHF.Lo | 0.89400 | 6.896106e-01 | -6.470927 | -6.402829 | -6.471637 | -6.443557 | 7.713765e-01 | 1 |
| USDCHF | iGARCH | 2015-02-02 | USDCHF.Lo | 0.92000 | 7.319616e-01 | -6.350835 | -6.255235 | -6.352225 | -6.312407 | 7.956105e-01 | 1 |
| USDCHF | csGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.193636e+00 | -6.688153 | -6.579196 | -6.689945 | -6.644361 | 1.404278e+00 | 1 |
| USDCHF | csGARCH | 2015-01-22 | USDCHF.Lo | 0.85300 | 1.141360e+00 | -6.534724 | -6.425767 | -6.536516 | -6.490932 | 1.338054e+00 | 1 |
| USDCHF | csGARCH | 2015-01-23 | USDCHF.Lo | 0.86800 | 6.200740e-01 | -6.493151 | -6.384194 | -6.494943 | -6.449359 | 7.143710e-01 | 1 |
| USDCAD | fGARCH.NGARCH | 2015-02-05 | USDCAD.Hi | 1.25800 | -2.752758e+42 | -487.602382 | -487.425326 | -487.607002 | -487.531219 | 2.188202e+42 | 1 |
| USDCAD | fGARCH.NGARCH | 2015-02-09 | USDCAD.Cl | 1.25170 | -7.979335e+22 | 142.673774 | 142.783031 | 142.671968 | 142.717692 | 6.374798e+22 | 1 |
| USDCAD | fGARCH.NGARCH | 2015-03-29 | USDCAD.Hi | 1.27000 | -6.542943e+22 | -529.240306 | -529.131049 | -529.242112 | -529.196389 | 5.151924e+22 | 1 |
| USDCAD | fGARCH.NGARCH | 2015-07-21 | USDCAD.Hi | 1.30500 | 4.139802e+61 | -435.142670 | -435.006474 | -435.145443 | -435.087930 | 3.172262e+61 | 1 |
| USDCAD | fGARCH.NGARCH | 2016-05-01 | USDCAD.Op | 1.25400 | -6.113225e+60 | -292.286659 | -292.081235 | -292.292844 | -292.204076 | 4.874980e+60 | 1 |
| USDCAD | fGARCH.NGARCH | 2016-05-02 | USDCAD.Hi | 1.27000 | 2.847428e+37 | -493.891329 | -493.741100 | -493.894693 | -493.830942 | 2.242069e+37 | 1 |
| USDCNY | sGARCH | 2014-07-10 | USDCNY.Lo | 2.20100 | 2.987751e+00 | -4.665480 | -4.583537 | -4.666505 | -4.632541 | 1.357452e+00 | 1 |
| USDCNY | fGARCH.GARCH | 2014-07-10 | USDCNY.Lo | 2.20100 | 2.987874e+00 | -4.665479 | -4.583536 | -4.666505 | -4.632541 | 1.357508e+00 | 1 |
| USDCNY | fGARCH.TGARCH | 2013-10-09 | USDCNY.Op | 6.11100 | 5.483283e+03 | 60.013013 | 60.135928 | 60.010739 | 60.062421 | 8.972808e+02 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-17 | USDCNY.Lo | 6.19200 | -3.142299e+01 | -584.776350 | -584.694407 | -584.777376 | -584.743412 | 5.074772e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-20 | USDCNY.Lo | 6.19500 | 1.601180e+01 | -588.464869 | -588.382700 | -588.465903 | -588.431836 | 2.584633e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-21 | USDCNY.Lo | 6.19300 | 1.802707e+02 | -584.204328 | -584.122385 | -584.205354 | -584.171390 | 2.910878e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-22 | USDCNY.Lo | 6.18900 | 6.023818e+01 | -586.383515 | -586.301572 | -586.384541 | -586.350577 | 9.733103e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-23 | USDCNY.Lo | 6.18200 | 1.116223e+02 | -582.294731 | -582.212788 | -582.295756 | -582.261792 | 1.805601e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-27 | USDCNY.Lo | 6.17600 | 4.872521e+01 | -587.187420 | -587.105250 | -587.188453 | -587.154387 | 7.889444e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-31 | USDCNY.Lo | 6.16300 | -1.151893e+02 | -587.546128 | -587.464185 | -587.547153 | -587.513189 | 1.869046e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-03 | USDCNY.Lo | 6.16800 | -1.481046e+00 | -591.735377 | -591.653208 | -591.736411 | -591.702344 | 2.401177e-01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-04 | USDCNY.Lo | 6.16100 | 1.118689e+01 | -590.853714 | -590.771771 | -590.854740 | -590.820775 | 1.815759e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-05 | USDCNY.Lo | 6.15300 | -5.459669e+01 | -563.148807 | -563.066864 | -563.149833 | -563.115869 | 8.873182e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-06 | USDCNY.Lo | 6.14700 | 2.635122e+01 | -591.728569 | -591.646626 | -591.729595 | -591.695631 | 4.286842e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-10 | USDCNY.Lo | 6.14400 | 5.336958e+01 | -588.785684 | -588.703514 | -588.786717 | -588.752651 | 8.686456e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-13 | USDCNY.Lo | 6.14200 | 4.004231e+02 | -583.022533 | -582.940590 | -583.023559 | -582.989595 | 6.519425e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-14 | USDCNY.Lo | 6.13600 | 4.872331e+01 | -586.351874 | -586.269931 | -586.352899 | -586.318935 | 7.940565e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-18 | USDCNY.Lo | 6.12700 | 4.620441e+00 | -583.267547 | -583.185604 | -583.268572 | -583.234608 | 7.541114e-01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-19 | USDCNY.Lo | 6.13000 | 3.981759e+01 | -587.532975 | -587.451032 | -587.534000 | -587.500036 | 6.495529e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-20 | USDCNY.Lo | 6.13000 | 1.169769e+02 | -586.017467 | -585.935524 | -586.018492 | -585.984528 | 1.908270e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-21 | USDCNY.Lo | 6.14100 | 5.744849e+01 | -586.508501 | -586.426558 | -586.509527 | -586.475563 | 9.354907e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-24 | USDCNY.Lo | 6.14000 | -3.247607e+01 | -589.174302 | -589.092132 | -589.175335 | -589.141269 | 5.289262e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-26 | USDCNY.Lo | 6.13300 | 9.738678e+01 | -587.251542 | -587.169599 | -587.252568 | -587.218604 | 1.587914e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-31 | USDCNY.Lo | 6.12900 | 2.545583e+02 | -584.923023 | -584.840853 | -584.924056 | -584.889989 | 4.153341e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-02 | USDCNY.Lo | 6.13100 | 1.578343e+00 | -590.429012 | -590.347069 | -590.430038 | -590.396074 | 2.574364e-01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-03 | USDCNY.Lo | 6.12500 | 3.759315e+01 | -581.281528 | -581.199585 | -581.282554 | -581.248590 | 6.137657e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-04 | USDCNY.Lo | 6.12800 | -4.565334e+01 | -589.259505 | -589.177562 | -589.260531 | -589.226567 | 7.449958e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-07 | USDCNY.Lo | 6.13000 | 7.649639e+01 | -580.676871 | -580.594702 | -580.677904 | -580.643838 | 1.247902e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-08 | USDCNY.Lo | 6.12200 | -2.517129e+01 | -587.872377 | -587.790434 | -587.873402 | -587.839438 | 4.111612e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-11 | USDCNY.Lo | 6.12000 | -3.251440e+01 | -587.456738 | -587.374795 | -587.457764 | -587.423800 | 5.312810e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-14 | USDCNY.Lo | 6.12500 | -1.796358e+02 | -584.617601 | -584.535431 | -584.618634 | -584.584568 | 2.932830e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-15 | USDCNY.Lo | 6.13200 | -1.112814e+01 | -590.468673 | -590.386730 | -590.469698 | -590.435734 | 1.814765e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-16 | USDCNY.Lo | 6.12900 | -1.759094e+02 | -585.597533 | -585.515590 | -585.598558 | -585.564594 | 2.870116e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-21 | USDCNY.Lo | 6.12800 | -2.039517e+01 | -588.488512 | -588.406343 | -588.489546 | -588.455479 | 3.328194e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-23 | USDCNY.Lo | 6.12400 | 1.512941e+01 | -590.152856 | -590.070913 | -590.153882 | -590.119918 | 2.470511e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-30 | USDCNY.Lo | 6.12800 | 1.553160e+02 | -567.572804 | -567.490861 | -567.573830 | -567.539866 | 2.534531e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-10-01 | USDCNY.Lo | 6.12800 | -1.146657e+02 | -584.091459 | -584.009516 | -584.092485 | -584.058521 | 1.871177e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-10-06 | USDCNY.Lo | 6.12900 | 2.295707e+02 | -583.286508 | -583.204565 | -583.287534 | -583.253570 | 3.745647e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-10-07 | USDCNY.Lo | 6.12500 | 5.146397e+01 | -565.845084 | -565.763141 | -565.846110 | -565.812146 | 8.402281e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-10-09 | USDCNY.Lo | 6.12000 | 6.182692e+01 | -583.758544 | -583.676826 | -583.759562 | -583.725700 | 1.010244e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-11-26 | USDCNY.Lo | 6.12300 | 6.187566e+01 | -583.601907 | -583.520189 | -583.602924 | -583.569062 | 1.010545e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2017-06-15 | USDCNY.Op | 6.80600 | -1.649282e+44 | -461.947546 | -461.824970 | -461.949803 | -461.898280 | 2.423276e+43 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-07-10 | USDCNY.Lo | 2.20100 | 2.977219e+00 | -4.669064 | -4.573464 | -4.670453 | -4.630636 | 1.352666e+00 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-07-24 | USDCNY.Lo | 6.18200 | -3.603032e+02 | 14.561667 | 14.643610 | 14.560642 | 14.594606 | 5.828262e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-07-29 | USDCNY.Lo | 6.16200 | -3.579216e+02 | 14.548624 | 14.630567 | 14.547598 | 14.581562 | 5.808530e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-07-31 | USDCNY.Lo | 6.16300 | -3.531901e+02 | 14.522470 | 14.604413 | 14.521444 | 14.555409 | 5.730814e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-08-04 | USDCNY.Lo | 6.16100 | -3.492923e+02 | 14.548440 | 14.630382 | 14.547414 | 14.581378 | 5.669409e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-08-26 | USDCNY.Lo | 6.13300 | 4.865151e+00 | 104.667516 | 104.749459 | 104.666490 | 104.700454 | 7.932742e-01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-09-04 | USDCNY.Lo | 6.12800 | 4.796821e+02 | 172.167572 | 172.249515 | 172.166546 | 172.200510 | 7.827710e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-10-19 | USDCNY.Lo | 6.11300 | -3.344848e+02 | 98.972743 | 99.054686 | 98.971717 | 99.005682 | 5.471696e+01 | 1 |
| USDCNY | fGARCH.APARCH | 2013-10-29 | USDCNY.Hi | 6.13400 | 2.876649e+25 | -526.990144 | -526.826258 | -526.994129 | -526.924267 | 4.689679e+24 | 1 |
| USDCNY | fGARCH.APARCH | 2013-11-07 | USDCNY.Hi | 6.14400 | -8.647337e+68 | -406.983178 | -406.819292 | -406.987163 | -406.917301 | 1.407444e+68 | 1 |
| USDCNY | fGARCH.GJRGARCH | 2014-07-10 | USDCNY.Lo | 2.20100 | 2.979918e+00 | -4.677596 | -4.581996 | -4.678985 | -4.639168 | 1.353893e+00 | 1 |
| USDCNY | fGARCH.GJRGARCH | 2014-09-01 | USDCNY.Lo | 6.13200 | 1.263740e+01 | 98.054293 | 98.136236 | 98.053267 | 98.087231 | 2.060893e+00 | 1 |
| USDCNY | fGARCH.GJRGARCH | 2014-11-12 | USDCNY.Lo | 6.11400 | -3.508494e+01 | 94.016565 | 94.098283 | 94.015548 | 94.049410 | 5.738460e+00 | 1 |
| USDCNY | fGARCH.ALLGARCH | 2013-03-19 | USDCNY.Op | 6.21400 | 1.851958e+30 | -506.919310 | -506.755875 | -506.923266 | -506.853622 | 2.980300e+29 | 1 |
| USDCNY | eGARCH | 2014-07-10 | USDCNY.Lo | 2.20100 | 2.758887e+00 | -4.752441 | -4.656841 | -4.753830 | -4.714013 | 1.253470e+00 | 1 |
| USDCNY | gjrGARCH | 2014-07-10 | USDCNY.Lo | 2.20100 | 2.894085e+00 | -4.702450 | -4.606850 | -4.703839 | -4.664022 | 1.314895e+00 | 1 |
| USDCNY | iGARCH | 2014-07-10 | USDCNY.Lo | 2.20100 | 2.988228e+00 | -4.673441 | -4.605156 | -4.674157 | -4.645993 | 1.357668e+00 | 1 |
| USDCNY | csGARCH | 2014-03-19 | USDCNY.Op | 6.18200 | -4.743008e+149 | 761.606011 | 761.769897 | 761.602025 | 761.671888 | 7.672287e+148 | 1 |
| USDJPY | fGARCH.TGARCH | 2013-03-31 | USDJPY.Op | 94.26200 | -5.215159e+89 | 433.750440 | 433.914326 | 433.746455 | 433.816317 | 5.532621e+87 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-05-20 | USDJPY.Hi | 102.87200 | 1.639729e+20 | 126.895461 | 127.031657 | 126.892687 | 126.950201 | 1.593951e+18 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-06-16 | USDJPY.Hi | 95.10600 | -2.728130e+05 | 179.131969 | 179.268541 | 179.129175 | 179.186867 | 2.868516e+03 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-06-17 | USDJPY.Hi | 95.75300 | 3.511368e+02 | 10.570756 | 10.706952 | 10.567983 | 10.625496 | 3.667111e+00 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-06-19 | USDJPY.Hi | 98.23900 | 4.076553e+124 | 740.361014 | 740.497210 | 740.358240 | 740.415754 | 4.149628e+122 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-07-01 | USDJPY.Hi | 100.43800 | 4.397652e+23 | -244.819452 | -244.683255 | -244.822225 | -244.764711 | 4.378474e+21 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-07-22 | USDJPY.Hi | 100.17000 | -7.099425e+16 | 107.520826 | 107.657022 | 107.518052 | 107.575566 | 7.087376e+14 | 1 |
| USDJPY | fGARCH.APARCH | 2013-02-07 | USDJPY.Lo | 93.09300 | -3.970675e+14 | -210.537651 | -210.401828 | -210.540404 | -210.483067 | 4.265278e+12 | 1 |
| USDJPY | fGARCH.APARCH | 2013-03-29 | USDJPY.Hi | 94.25500 | 1.067074e+03 | -571.141577 | -570.936720 | -571.147717 | -571.059231 | 1.132114e+01 | 1 |
| USDJPY | fGARCH.APARCH | 2013-05-13 | USDJPY.Hi | 102.26100 | 1.875536e+63 | -401.564171 | -401.441594 | -401.566428 | -401.514904 | 1.834068e+61 | 1 |
| USDJPY | fGARCH.APARCH | 2013-06-12 | USDJPY.Hi | 95.93000 | -1.338837e+49 | 118.941807 | 119.091623 | 118.938467 | 119.002021 | 1.395639e+47 | 1 |
| USDJPY | fGARCH.ALLGARCH | 2013-04-08 | USDJPY.Lo | 98.63900 | 2.419383e+10 | -45.341071 | -45.164015 | -45.345691 | -45.269908 | 2.452765e+08 | 1 |
| USDJPY | fGARCH.ALLGARCH | 2013-04-14 | USDJPY.Lo | 97.62300 | 1.365824e+02 | 9.689241 | 9.866784 | 9.684586 | 9.760608 | 1.399080e+00 | 1 |
| USDJPY | fGARCH.ALLGARCH | 2013-05-15 | USDJPY.Lo | 101.85000 | 1.719010e+30 | -497.287445 | -497.124010 | -497.291401 | -497.221757 | 1.687786e+28 | 1 |
| USDJPY | fGARCH.ALLGARCH | 2013-05-15 | USDJPY.Cl | 102.25800 | 6.921087e+61 | 309.378416 | 309.555471 | 309.373795 | 309.449578 | 6.768259e+59 | 1 |
| USDJPY | fGARCH.ALLGARCH | 2013-06-19 | USDJPY.Lo | 96.21100 | -8.650911e+03 | 78.994799 | 79.117376 | 78.992542 | 79.044066 | 8.991603e+01 | 1 |
| USDJPY | fGARCH.ALLGARCH | 2013-12-03 | USDJPY.Hi | 103.36900 | 3.656304e+138 | -201.516514 | -201.352628 | -201.520499 | -201.450637 | 3.537137e+136 | 1 |
| USDJPY | fGARCH.ALLGARCH | 2013-12-12 | USDJPY.Hi | 103.07700 | -3.572408e+44 | 285.951103 | 286.128646 | 285.946448 | 286.022470 | 3.465767e+42 | 1 |
| USDJPY | eGARCH | 2013-03-19 | USDJPY.Lo | 94.77000 | 2.936350e+60 | 155.742660 | 155.919716 | 155.738040 | 155.813823 | 3.098396e+58 | 1 |
| USDJPY | eGARCH | 2013-04-07 | USDJPY.Hi | 99.01600 | -1.249428e+80 | 167.045855 | 167.196083 | 167.042490 | 167.106242 | 1.261845e+78 | 1 |
| USDJPY | eGARCH | 2013-04-14 | USDJPY.Lo | 97.62300 | -5.344121e+15 | 115.987973 | 116.138202 | 115.984609 | 116.048361 | 5.474244e+13 | 1 |
| USDJPY | eGARCH | 2013-05-13 | USDJPY.Hi | 102.26100 | 1.483098e+63 | 161.813922 | 161.922879 | 161.812130 | 161.857714 | 1.450307e+61 | 1 |
| USDJPY | eGARCH | 2013-06-16 | USDJPY.Hi | 95.10600 | 2.867306e+54 | 123.668672 | 123.805244 | 123.665878 | 123.723570 | 3.014853e+52 | 1 |
| USDJPY | eGARCH | 2013-11-18 | USDJPY.Hi | 100.33300 | -1.192013e+13 | 283.354744 | 283.491693 | 283.351929 | 283.409799 | 1.188057e+11 | 1 |
| USDJPY | apARCH | 2013-01-29 | USDJPY.Hi | 90.99000 | -1.175138e+50 | -1305.505004 | -1305.341568 | -1305.508959 | -1305.439315 | 1.291503e+48 | 1 |
| USDJPY | apARCH | 2013-03-15 | USDJPY.Lo | 95.16000 | -1.758223e+61 | 315.688639 | 315.824835 | 315.685866 | 315.743379 | 1.847649e+59 | 1 |
| USDJPY | apARCH | 2013-04-04 | USDJPY.Lo | 95.81700 | 6.156224e+02 | 8.903971 | 9.094646 | 8.898637 | 8.980607 | 6.424981e+00 | 1 |
| USDJPY | apARCH | 2013-04-09 | USDJPY.Hi | 99.69400 | -7.412985e+02 | -1357.528473 | -1357.392277 | -1357.531246 | -1357.473733 | 7.435739e+00 | 1 |
| USDJPY | apARCH | 2013-04-17 | USDJPY.Lo | 97.64000 | -4.147166e+22 | -1334.100214 | -1333.950398 | -1334.103553 | -1334.039999 | 4.247405e+20 | 1 |
| USDJPY | apARCH | 2013-05-06 | USDJPY.Op | 99.36400 | -2.666861e+24 | 223.445230 | 223.595046 | 223.441891 | 223.505445 | 2.683931e+22 | 1 |
| USDJPY | apARCH | 2013-05-09 | USDJPY.Hi | 101.94900 | -3.960522e+122 | 494.605046 | 494.727623 | 494.602789 | 494.654312 | 3.884807e+120 | 1 |
| USDJPY | apARCH | 2013-05-14 | USDJPY.Hi | 102.76000 | 6.892843e+01 | -1352.815761 | -1352.652325 | -1352.819717 | -1352.750072 | 6.707710e-01 | 1 |
| USDJPY | apARCH | 2013-05-15 | USDJPY.Cl | 102.25800 | -4.614626e+04 | 12.698392 | 12.861828 | 12.694436 | 12.764081 | 4.512728e+02 | 1 |
6.1.1.1D : Table Contain Bias dataset.
Now we try to filter the dataset which contain OHLC of 7 currecies.
## Bias which contain OHLC of 7 currencies.
acc <- fx %>% dplyr::filter(Date %in% ntimeID2) %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 0.0000000 | 4 | 2.000000 | 0.0042571 | -7.7157954 | -7.6442923 | -7.7165827 | -7.6870568 |
| USDAUD | fGARCH.GARCH | 0.0000000 | 4 | 2.000000 | 0.0042571 | -7.7157308 | -7.6442277 | -7.7165180 | -7.6869921 |
| USDAUD | fGARCH.TGARCH | 0.0000000 | 4 | 2.000000 | 0.0040899 | -7.7115975 | -7.6264748 | -7.7127056 | -7.6773848 |
| USDAUD | fGARCH.AVGARCH | 0.0000000 | 4 | 2.000000 | 0.0046426 | -7.7096123 | -7.6108700 | -7.7110944 | -7.6699256 |
| USDAUD | fGARCH.NGARCH | 0.0000000 | 4 | 2.000000 | 0.0042573 | -7.7086240 | -7.6235013 | -7.7097321 | -7.6744113 |
| USDAUD | fGARCH.NAGARCH | 0.0000000 | 4 | 2.000000 | 0.0044076 | -7.7252460 | -7.6401232 | -7.7263541 | -7.6910333 |
| USDAUD | fGARCH.APARCH | 0.0000000 | 4 | 2.000000 | 0.0045248 | -7.7121329 | -7.6133905 | -7.7136150 | -7.6724462 |
| USDAUD | fGARCH.GJRGARCH | 0.0000000 | 4 | 2.000000 | 0.0045302 | -7.7194559 | -7.6343332 | -7.7205640 | -7.6852432 |
| USDAUD | fGARCH.ALLGARCH | 0.0000000 | 4 | 2.000000 | 0.0046029 | -7.7114799 | -7.5991179 | -7.7133882 | -7.6663191 |
| USDAUD | eGARCH | 0.0000000 | 4 | 2.000000 | 0.0043887 | -7.7275210 | -7.6423983 | -7.7286292 | -7.6933084 |
| USDAUD | gjrGARCH | 0.0000000 | 4 | 2.000000 | 0.0045379 | -7.7195102 | -7.6343875 | -7.7206184 | -7.6852975 |
| USDAUD | apARCH | 0.0000000 | 4 | 2.000000 | 0.0045312 | -7.7121916 | -7.6134493 | -7.7136737 | -7.6725049 |
| USDAUD | iGARCH | 0.0000000 | 4 | 2.000000 | 0.0041693 | -7.7214244 | -7.6635410 | -7.7219447 | -7.6981598 |
| USDAUD | csGARCH | 0.0000000 | 4 | 2.000000 | 0.0045144 | -7.7006430 | -7.6019007 | -7.7021251 | -7.6609563 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 0.0000000 | 4 | 2.000000 | 0.6050811 | -7.6998813 | -7.5943291 | -7.7017000 | -7.6574575 |
| USDEUR | fGARCH.GARCH | 0.0000000 | 4 | 2.000000 | 0.6048705 | -7.6997431 | -7.5941909 | -7.7015618 | -7.6573194 |
| USDEUR | fGARCH.TGARCH | 0.0000000 | 4 | 2.000000 | 0.2397655 | -7.6699895 | -7.5508176 | -7.6722585 | -7.6220917 |
| USDEUR | fGARCH.AVGARCH | 0.0000001 | 4 | 2.000000 | 0.3127196 | -7.8253571 | -7.6925656 | -7.8281276 | -7.7719853 |
| USDEUR | fGARCH.NGARCH | 0.0000001 | 4 | 2.000000 | 0.2303104 | -7.8613915 | -7.7422197 | -7.8636606 | -7.8134938 |
| USDEUR | fGARCH.NAGARCH | 0.0000000 | 4 | 2.000000 | 0.4971729 | -7.7737017 | -7.6545298 | -7.7759707 | -7.7258039 |
| USDEUR | fGARCH.APARCH | 0.0000000 | 4 | 2.000000 | 0.3255517 | -7.8170471 | -7.6842556 | -7.8198177 | -7.7636753 |
| USDEUR | fGARCH.GJRGARCH | 0.0000000 | 4 | 2.000000 | 0.6011446 | -7.7266217 | -7.6074498 | -7.7288907 | -7.6787239 |
| USDEUR | fGARCH.ALLGARCH | 0.0000001 | 4 | 2.000000 | 0.2042237 | -7.8817577 | -7.7353466 | -7.8850803 | -7.8229118 |
| USDEUR | eGARCH | 0.0000000 | 4 | 2.000000 | 0.0294717 | -8.1069604 | -7.9877886 | -8.1092294 | -8.0590626 |
| USDEUR | gjrGARCH | 0.0000001 | 4 | 2.000000 | 0.6060193 | -7.7316377 | -7.6124659 | -7.7339067 | -7.6837399 |
| USDEUR | apARCH | 0.0000000 | 4 | 2.000000 | 0.2455494 | -7.8656406 | -7.7328491 | -7.8684111 | -7.8122688 |
| USDEUR | iGARCH | 0.0000000 | 4 | 2.000000 | 0.5011615 | -7.7435079 | -7.6515754 | -7.7449283 | -7.7065582 |
| USDEUR | csGARCH | 0.0000000 | 4 | 2.000000 | 0.0428158 | -8.0263288 | -7.8935374 | -8.0290994 | -7.9729571 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 0.0000001 | 4 | 2.000000 | 0.8403505 | -8.7045263 | -8.6332190 | -8.7053077 | -8.6758696 |
| USDGBP | fGARCH.GARCH | 0.0000001 | 4 | 2.000000 | 0.8403599 | -8.7045383 | -8.6332310 | -8.7053197 | -8.6758816 |
| USDGBP | fGARCH.TGARCH | 0.0000000 | 4 | 2.000000 | 0.5772550 | -8.6611404 | -8.5762508 | -8.6622403 | -8.6270253 |
| USDGBP | fGARCH.AVGARCH | 0.0000000 | 4 | 2.000000 | 0.4602830 | -8.4926470 | -8.3941751 | -8.4941180 | -8.4530735 |
| USDGBP | fGARCH.NGARCH | 0.0000000 | 4 | 2.000000 | 0.6589618 | -8.7556480 | -8.6707584 | -8.7567478 | -8.7215329 |
| USDGBP | fGARCH.NAGARCH | 0.0000000 | 4 | 2.000000 | 0.0812317 | -9.0784271 | -8.9935375 | -9.0795270 | -9.0443120 |
| USDGBP | fGARCH.APARCH | 0.0000000 | 4 | 2.000000 | 0.6407555 | -8.7652475 | -8.6667756 | -8.7667186 | -8.7256740 |
| USDGBP | fGARCH.GJRGARCH | 0.0000000 | 4 | 2.000000 | 0.8314076 | -8.7097255 | -8.6248359 | -8.7108253 | -8.6756104 |
| USDGBP | fGARCH.ALLGARCH | 0.0000000 | 4 | 2.000000 | 0.0625439 | -9.0894691 | -8.9774148 | -9.0913632 | -9.0444371 |
| USDGBP | eGARCH | 0.0000000 | 4 | 2.000000 | 0.0688022 | -9.1094499 | -9.0245603 | -9.1105498 | -9.0753348 |
| USDGBP | gjrGARCH | 0.0000000 | 4 | 2.000000 | 0.0753793 | -9.0831765 | -8.9982869 | -9.0842764 | -9.0490614 |
| USDGBP | apARCH | 0.0000000 | 4 | 2.000000 | 0.5934160 | -8.7853142 | -8.6868422 | -8.7867852 | -8.7457406 |
| USDGBP | iGARCH | 0.0000000 | 4 | 2.000000 | 0.9567749 | -8.6735138 | -8.6157889 | -8.6740302 | -8.6503156 |
| USDGBP | csGARCH | 0.0000000 | 4 | 2.000000 | 0.1128146 | -9.0261227 | -8.9276507 | -9.0275937 | -8.9865491 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 0.0000001 | 4 | 2.000000 | 0.0237947 | -7.8898857 | -7.7905975 | -7.8915229 | -7.8499705 |
| USDCHF | fGARCH.GARCH | 0.0000001 | 4 | 2.000000 | 0.0238168 | -7.8898457 | -7.7905575 | -7.8914829 | -7.8499305 |
| USDCHF | fGARCH.TGARCH | 0.0000000 | 4 | 2.000000 | 0.0232968 | -7.7798803 | -7.6668972 | -7.7819483 | -7.7344596 |
| USDCHF | fGARCH.AVGARCH | 0.0000001 | 4 | 2.000000 | 0.0224723 | -7.8728367 | -7.7461586 | -7.8753878 | -7.8219104 |
| USDCHF | fGARCH.NGARCH | 0.0000003 | 4 | 2.000000 | 0.0219593 | -7.8762987 | -7.7633156 | -7.8783667 | -7.8308780 |
| USDCHF | fGARCH.NAGARCH | 0.0000001 | 4 | 2.000000 | 0.0217284 | -7.8960491 | -7.7830660 | -7.8981171 | -7.8506284 |
| USDCHF | fGARCH.APARCH | 0.0000001 | 4 | 2.000000 | 0.0194777 | -7.7981621 | -7.6714840 | -7.8007132 | -7.7472358 |
| USDCHF | fGARCH.GJRGARCH | 0.0000001 | 4 | 2.000000 | 0.0214671 | -7.8973560 | -7.7843728 | -7.8994240 | -7.8519353 |
| USDCHF | fGARCH.ALLGARCH | 0.0000002 | 4 | 2.000000 | 0.0184411 | -7.8761116 | -7.7357386 | -7.8791975 | -7.8196798 |
| USDCHF | eGARCH | 0.0000001 | 4 | 2.000000 | 0.0194239 | -7.9009921 | -7.7880089 | -7.9030600 | -7.8555713 |
| USDCHF | gjrGARCH | 0.0000003 | 4 | 2.000000 | 0.0176093 | -7.8932971 | -7.7803140 | -7.8953651 | -7.8478764 |
| USDCHF | apARCH | 0.0000002 | 4 | 2.000000 | 0.0175526 | -7.8837665 | -7.7570884 | -7.8863176 | -7.8328402 |
| USDCHF | iGARCH | 0.0000003 | 4 | 2.000000 | 0.0198707 | -7.8801376 | -7.7945442 | -7.8813971 | -7.8457279 |
| USDCHF | csGARCH | 0.0000001 | 4 | 2.000000 | 0.0201152 | -7.8635773 | -7.7368992 | -7.8661284 | -7.8126510 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 0.0000000 | 4 | 2.000000 | 0.0049855 | -8.2818931 | -8.2069851 | -8.2827573 | -8.2517860 |
| USDCAD | fGARCH.GARCH | 0.0000000 | 4 | 2.000000 | 0.0049738 | -8.2817294 | -8.2068214 | -8.2825936 | -8.2516222 |
| USDCAD | fGARCH.TGARCH | 0.0000000 | 4 | 2.000000 | 0.0051920 | -8.2981108 | -8.2095831 | -8.2993091 | -8.2625296 |
| USDCAD | fGARCH.AVGARCH | 0.0000000 | 4 | 2.000000 | 0.0929052 | -8.1148285 | -8.0126812 | -8.1164139 | -8.0737733 |
| USDCAD | fGARCH.NGARCH | 0.0000000 | 4 | 2.000000 | 0.0048273 | -8.2735840 | -8.1850564 | -8.2747824 | -8.2380029 |
| USDCAD | fGARCH.NAGARCH | 0.0000000 | 4 | 2.000000 | 0.0037520 | -8.2868248 | -8.1982972 | -8.2880231 | -8.2512436 |
| USDCAD | fGARCH.APARCH | 0.0000000 | 4 | 2.000000 | 0.0508286 | -8.1477858 | -8.0456386 | -8.1493712 | -8.1067306 |
| USDCAD | fGARCH.GJRGARCH | 0.0000000 | 4 | 2.000000 | 0.0032447 | -8.2888576 | -8.2003299 | -8.2900559 | -8.2532764 |
| USDCAD | fGARCH.ALLGARCH | 0.0000001 | 4 | 2.000000 | 0.0040514 | -8.2748314 | -8.1590645 | -8.2768561 | -8.2283022 |
| USDCAD | eGARCH | 0.0000001 | 4 | 2.000000 | 0.0050232 | -8.2940264 | -8.2054988 | -8.2952247 | -8.2584452 |
| USDCAD | gjrGARCH | 0.0000000 | 4 | 2.000000 | 0.0032165 | -8.2887046 | -8.2001769 | -8.2899029 | -8.2531234 |
| USDCAD | apARCH | 0.0000000 | 4 | 2.000000 | 0.0037201 | -8.2824580 | -8.1803107 | -8.2840434 | -8.2414028 |
| USDCAD | iGARCH | 0.0000000 | 4 | 2.000000 | 0.0046769 | -8.2861995 | -8.2249111 | -8.2867831 | -8.2615663 |
| USDCAD | csGARCH | 0.0000000 | 4 | 2.000000 | 0.0049357 | -8.2689115 | -8.1667643 | -8.2704970 | -8.2278563 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 0.0000005 | 4 | 2.000000 | 0.0055601 | -6.9273647 | -6.8356839 | -6.9286566 | -6.8905204 |
| USDCNY | fGARCH.GARCH | 0.0000005 | 4 | 2.000000 | 0.0055601 | -6.9273648 | -6.8356840 | -6.9286567 | -6.8905205 |
| USDCNY | fGARCH.TGARCH | 0.0000008 | 4 | 2.000000 | 0.0048566 | -6.8925111 | -6.7872481 | -6.8942002 | -6.8502084 |
| USDCNY | fGARCH.AVGARCH | 0.0000005 | 4 | 2.000000 | 0.0111231 | -6.9095713 | -6.7907259 | -6.9117090 | -6.8618102 |
| USDCNY | fGARCH.NGARCH | 0.0000004 | 4 | 2.000000 | 0.0048438 | -6.9226063 | -6.8173432 | -6.9242953 | -6.8803036 |
| USDCNY | fGARCH.NAGARCH | 0.0000005 | 4 | 2.000000 | 0.0050575 | -6.9179916 | -6.8127285 | -6.9196806 | -6.8756888 |
| USDCNY | fGARCH.APARCH | 0.0000004 | 4 | 2.000000 | 0.0048932 | -6.9185218 | -6.7996764 | -6.9206595 | -6.8707607 |
| USDCNY | fGARCH.GJRGARCH | 0.0000005 | 4 | 2.000000 | 0.0049980 | -6.9182496 | -6.8129865 | -6.9199386 | -6.8759469 |
| USDCNY | fGARCH.ALLGARCH | 0.0000006 | 4 | 2.000000 | 0.0049341 | -6.9226321 | -6.7902043 | -6.9252692 | -6.8694125 |
| USDCNY | eGARCH | 0.0000004 | 4 | 2.000000 | 0.0044761 | -6.8891119 | -6.7838488 | -6.8908009 | -6.8468092 |
| USDCNY | gjrGARCH | 0.0000005 | 4 | 2.000000 | 0.0049979 | -6.9182497 | -6.8129866 | -6.9199387 | -6.8759470 |
| USDCNY | apARCH | 0.0000004 | 4 | 2.000000 | 0.0050421 | -6.9182851 | -6.7994396 | -6.9204227 | -6.8705239 |
| USDCNY | iGARCH | 0.0000006 | 4 | 2.000000 | 0.0051785 | -6.9005154 | -6.8224169 | -6.9014626 | -6.8691295 |
| USDCNY | csGARCH | 0.0000005 | 4 | 2.000000 | 0.0055494 | -6.9114237 | -6.7925783 | -6.9135614 | -6.8636626 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 0.0043414 | 4 | 1.997829 | 0.0272442 | 0.8165514 | 0.9014410 | 0.8154383 | 0.8506665 |
| USDJPY | fGARCH.GARCH | 0.0043414 | 4 | 1.997829 | 0.0272442 | 0.8165514 | 0.9014410 | 0.8154383 | 0.8506665 |
| USDJPY | fGARCH.TGARCH | 0.0042872 | 4 | 1.997856 | 0.0280165 | 0.7848311 | 0.8833030 | 0.7833470 | 0.8244046 |
| USDJPY | fGARCH.AVGARCH | 0.0043247 | 4 | 1.997838 | 0.0250116 | 0.7776130 | 0.8896673 | 0.7757060 | 0.8226450 |
| USDJPY | fGARCH.NGARCH | 0.0043057 | 4 | 1.997847 | 0.0311397 | 0.8114503 | 0.9099222 | 0.8099662 | 0.8510238 |
| USDJPY | fGARCH.NAGARCH | 0.0048188 | 4 | 1.997591 | 0.0260458 | 0.7715537 | 0.8700256 | 0.7700696 | 0.8111272 |
| USDJPY | fGARCH.APARCH | 0.0045436 | 4 | 1.997728 | 0.0297432 | 0.7888246 | 0.9008789 | 0.7869176 | 0.8338565 |
| USDJPY | fGARCH.GJRGARCH | 0.0043442 | 4 | 1.997828 | 0.0268770 | 0.7971652 | 0.8956372 | 0.7956812 | 0.8367387 |
| USDJPY | fGARCH.ALLGARCH | 0.0019024 | 4 | 1.999049 | 0.0263061 | 0.7644200 | 0.8900566 | 0.7620388 | 0.8149104 |
| USDJPY | eGARCH | 0.0041875 | 4 | 1.997906 | 0.0278439 | 0.7416013 | 0.8400733 | 0.7401173 | 0.7811748 |
| USDJPY | gjrGARCH | 0.0047415 | 4 | 1.997629 | 0.0263785 | 0.7701763 | 0.8686482 | 0.7686922 | 0.8097498 |
| USDJPY | apARCH | 0.0051226 | 4 | 1.997439 | 0.0298260 | 0.7886781 | 0.9007324 | 0.7867711 | 0.8337100 |
| USDJPY | iGARCH | 0.0043089 | 4 | 1.997845 | 0.0271791 | 0.8196221 | 0.8909294 | 0.8188273 | 0.8482788 |
| USDJPY | csGARCH | 0.0042846 | 4 | 1.997858 | 0.0272044 | 0.8340534 | 0.9461076 | 0.8321463 | 0.8790853 |
6.1.1.2A : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 0.0006203 | 28 | 0.2856700 | 9.713449 | -6.628971 | -6.543381 | -6.630156 | -6.594571 |
| fGARCH.GARCH | 0.0006203 | 28 | 0.2856700 | 9.713274 | -6.628914 | -6.543324 | -6.630099 | -6.594514 |
| fGARCH.TGARCH | 0.0006126 | 28 | 0.2856705 | 9.486882 | -6.604057 | -6.504853 | -6.605616 | -6.564185 |
| fGARCH.AVGARCH | 0.0006179 | 28 | 0.2856701 | 9.383348 | -6.592463 | -6.479644 | -6.594449 | -6.547119 |
| fGARCH.NGARCH | 0.0006152 | 28 | 0.2856703 | 9.695058 | -6.655243 | -6.556039 | -6.656803 | -6.615371 |
| fGARCH.NAGARCH | 0.0006885 | 28 | 0.2856651 | 9.760064 | -6.700955 | -6.601751 | -6.702515 | -6.661083 |
| fGARCH.APARCH | 0.0006492 | 28 | 0.2856679 | 9.572200 | -6.624296 | -6.511477 | -6.626283 | -6.578952 |
| fGARCH.GJRGARCH | 0.0006207 | 28 | 0.2856700 | 9.687413 | -6.637586 | -6.538382 | -6.639145 | -6.597714 |
| fGARCH.ALLGARCH | 0.0002719 | 28 | 0.2856949 | 9.726224 | -6.713123 | -6.586690 | -6.715588 | -6.662307 |
| eGARCH | 0.0005983 | 28 | 0.2856716 | 9.767911 | -6.755209 | -6.656004 | -6.756768 | -6.715337 |
| gjrGARCH | 0.0006775 | 28 | 0.2856659 | 9.760039 | -6.694914 | -6.595710 | -6.696474 | -6.655042 |
| apARCH | 0.0007319 | 28 | 0.2856620 | 9.665221 | -6.665568 | -6.552750 | -6.667555 | -6.620224 |
| iGARCH | 0.0006157 | 28 | 0.2856703 | 9.714553 | -6.626525 | -6.554550 | -6.627388 | -6.597597 |
| csGARCH | 0.0006122 | 28 | 0.2856706 | 9.858674 | -6.708993 | -6.596175 | -6.710980 | -6.663650 |
6.1.1.2B : Table summary
| Model | n |
|---|---|
6.1.1.2C : Table summary number of errors.
| .id | Model | Date | Type | Price | Price.T1 | Akaike | Bayes | Shibata | Hannan.Quinn | diff | se |
|---|---|---|---|---|---|---|---|---|---|---|---|
6.1.1.2D : Table Contain Bias dataset.
Lastly, we filter all bias data and look at the comparison of mse of OHLC of 7 currencies.
## contain OHLC of 7 currencies without bias.
acc <- fx %>% dplyr::filter(Date %in% ntimeID2 & !Date %in% ntimeID) %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 0.0000000 | 4 | 2.000000 | 0.0042571 | -7.7157954 | -7.6442923 | -7.7165827 | -7.6870568 |
| USDAUD | fGARCH.GARCH | 0.0000000 | 4 | 2.000000 | 0.0042571 | -7.7157308 | -7.6442277 | -7.7165180 | -7.6869921 |
| USDAUD | fGARCH.TGARCH | 0.0000000 | 4 | 2.000000 | 0.0040899 | -7.7115975 | -7.6264748 | -7.7127056 | -7.6773848 |
| USDAUD | fGARCH.AVGARCH | 0.0000000 | 4 | 2.000000 | 0.0046426 | -7.7096123 | -7.6108700 | -7.7110944 | -7.6699256 |
| USDAUD | fGARCH.NGARCH | 0.0000000 | 4 | 2.000000 | 0.0042573 | -7.7086240 | -7.6235013 | -7.7097321 | -7.6744113 |
| USDAUD | fGARCH.NAGARCH | 0.0000000 | 4 | 2.000000 | 0.0044076 | -7.7252460 | -7.6401232 | -7.7263541 | -7.6910333 |
| USDAUD | fGARCH.APARCH | 0.0000000 | 4 | 2.000000 | 0.0045248 | -7.7121329 | -7.6133905 | -7.7136150 | -7.6724462 |
| USDAUD | fGARCH.GJRGARCH | 0.0000000 | 4 | 2.000000 | 0.0045302 | -7.7194559 | -7.6343332 | -7.7205640 | -7.6852432 |
| USDAUD | fGARCH.ALLGARCH | 0.0000000 | 4 | 2.000000 | 0.0046029 | -7.7114799 | -7.5991179 | -7.7133882 | -7.6663191 |
| USDAUD | eGARCH | 0.0000000 | 4 | 2.000000 | 0.0043887 | -7.7275210 | -7.6423983 | -7.7286292 | -7.6933084 |
| USDAUD | gjrGARCH | 0.0000000 | 4 | 2.000000 | 0.0045379 | -7.7195102 | -7.6343875 | -7.7206184 | -7.6852975 |
| USDAUD | apARCH | 0.0000000 | 4 | 2.000000 | 0.0045312 | -7.7121916 | -7.6134493 | -7.7136737 | -7.6725049 |
| USDAUD | iGARCH | 0.0000000 | 4 | 2.000000 | 0.0041693 | -7.7214244 | -7.6635410 | -7.7219447 | -7.6981598 |
| USDAUD | csGARCH | 0.0000000 | 4 | 2.000000 | 0.0045144 | -7.7006430 | -7.6019007 | -7.7021251 | -7.6609563 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 0.0000000 | 4 | 2.000000 | 0.6050811 | -7.6998813 | -7.5943291 | -7.7017000 | -7.6574575 |
| USDEUR | fGARCH.GARCH | 0.0000000 | 4 | 2.000000 | 0.6048705 | -7.6997431 | -7.5941909 | -7.7015618 | -7.6573194 |
| USDEUR | fGARCH.TGARCH | 0.0000000 | 4 | 2.000000 | 0.2397655 | -7.6699895 | -7.5508176 | -7.6722585 | -7.6220917 |
| USDEUR | fGARCH.AVGARCH | 0.0000001 | 4 | 2.000000 | 0.3127196 | -7.8253571 | -7.6925656 | -7.8281276 | -7.7719853 |
| USDEUR | fGARCH.NGARCH | 0.0000001 | 4 | 2.000000 | 0.2303104 | -7.8613915 | -7.7422197 | -7.8636606 | -7.8134938 |
| USDEUR | fGARCH.NAGARCH | 0.0000000 | 4 | 2.000000 | 0.4971729 | -7.7737017 | -7.6545298 | -7.7759707 | -7.7258039 |
| USDEUR | fGARCH.APARCH | 0.0000000 | 4 | 2.000000 | 0.3255517 | -7.8170471 | -7.6842556 | -7.8198177 | -7.7636753 |
| USDEUR | fGARCH.GJRGARCH | 0.0000000 | 4 | 2.000000 | 0.6011446 | -7.7266217 | -7.6074498 | -7.7288907 | -7.6787239 |
| USDEUR | fGARCH.ALLGARCH | 0.0000001 | 4 | 2.000000 | 0.2042237 | -7.8817577 | -7.7353466 | -7.8850803 | -7.8229118 |
| USDEUR | eGARCH | 0.0000000 | 4 | 2.000000 | 0.0294717 | -8.1069604 | -7.9877886 | -8.1092294 | -8.0590626 |
| USDEUR | gjrGARCH | 0.0000001 | 4 | 2.000000 | 0.6060193 | -7.7316377 | -7.6124659 | -7.7339067 | -7.6837399 |
| USDEUR | apARCH | 0.0000000 | 4 | 2.000000 | 0.2455494 | -7.8656406 | -7.7328491 | -7.8684111 | -7.8122688 |
| USDEUR | iGARCH | 0.0000000 | 4 | 2.000000 | 0.5011615 | -7.7435079 | -7.6515754 | -7.7449283 | -7.7065582 |
| USDEUR | csGARCH | 0.0000000 | 4 | 2.000000 | 0.0428158 | -8.0263288 | -7.8935374 | -8.0290994 | -7.9729571 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 0.0000001 | 4 | 2.000000 | 0.8403505 | -8.7045263 | -8.6332190 | -8.7053077 | -8.6758696 |
| USDGBP | fGARCH.GARCH | 0.0000001 | 4 | 2.000000 | 0.8403599 | -8.7045383 | -8.6332310 | -8.7053197 | -8.6758816 |
| USDGBP | fGARCH.TGARCH | 0.0000000 | 4 | 2.000000 | 0.5772550 | -8.6611404 | -8.5762508 | -8.6622403 | -8.6270253 |
| USDGBP | fGARCH.AVGARCH | 0.0000000 | 4 | 2.000000 | 0.4602830 | -8.4926470 | -8.3941751 | -8.4941180 | -8.4530735 |
| USDGBP | fGARCH.NGARCH | 0.0000000 | 4 | 2.000000 | 0.6589618 | -8.7556480 | -8.6707584 | -8.7567478 | -8.7215329 |
| USDGBP | fGARCH.NAGARCH | 0.0000000 | 4 | 2.000000 | 0.0812317 | -9.0784271 | -8.9935375 | -9.0795270 | -9.0443120 |
| USDGBP | fGARCH.APARCH | 0.0000000 | 4 | 2.000000 | 0.6407555 | -8.7652475 | -8.6667756 | -8.7667186 | -8.7256740 |
| USDGBP | fGARCH.GJRGARCH | 0.0000000 | 4 | 2.000000 | 0.8314076 | -8.7097255 | -8.6248359 | -8.7108253 | -8.6756104 |
| USDGBP | fGARCH.ALLGARCH | 0.0000000 | 4 | 2.000000 | 0.0625439 | -9.0894691 | -8.9774148 | -9.0913632 | -9.0444371 |
| USDGBP | eGARCH | 0.0000000 | 4 | 2.000000 | 0.0688022 | -9.1094499 | -9.0245603 | -9.1105498 | -9.0753348 |
| USDGBP | gjrGARCH | 0.0000000 | 4 | 2.000000 | 0.0753793 | -9.0831765 | -8.9982869 | -9.0842764 | -9.0490614 |
| USDGBP | apARCH | 0.0000000 | 4 | 2.000000 | 0.5934160 | -8.7853142 | -8.6868422 | -8.7867852 | -8.7457406 |
| USDGBP | iGARCH | 0.0000000 | 4 | 2.000000 | 0.9567749 | -8.6735138 | -8.6157889 | -8.6740302 | -8.6503156 |
| USDGBP | csGARCH | 0.0000000 | 4 | 2.000000 | 0.1128146 | -9.0261227 | -8.9276507 | -9.0275937 | -8.9865491 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 0.0000001 | 4 | 2.000000 | 0.0237947 | -7.8898857 | -7.7905975 | -7.8915229 | -7.8499705 |
| USDCHF | fGARCH.GARCH | 0.0000001 | 4 | 2.000000 | 0.0238168 | -7.8898457 | -7.7905575 | -7.8914829 | -7.8499305 |
| USDCHF | fGARCH.TGARCH | 0.0000000 | 4 | 2.000000 | 0.0232968 | -7.7798803 | -7.6668972 | -7.7819483 | -7.7344596 |
| USDCHF | fGARCH.AVGARCH | 0.0000001 | 4 | 2.000000 | 0.0224723 | -7.8728367 | -7.7461586 | -7.8753878 | -7.8219104 |
| USDCHF | fGARCH.NGARCH | 0.0000003 | 4 | 2.000000 | 0.0219593 | -7.8762987 | -7.7633156 | -7.8783667 | -7.8308780 |
| USDCHF | fGARCH.NAGARCH | 0.0000001 | 4 | 2.000000 | 0.0217284 | -7.8960491 | -7.7830660 | -7.8981171 | -7.8506284 |
| USDCHF | fGARCH.APARCH | 0.0000001 | 4 | 2.000000 | 0.0194777 | -7.7981621 | -7.6714840 | -7.8007132 | -7.7472358 |
| USDCHF | fGARCH.GJRGARCH | 0.0000001 | 4 | 2.000000 | 0.0214671 | -7.8973560 | -7.7843728 | -7.8994240 | -7.8519353 |
| USDCHF | fGARCH.ALLGARCH | 0.0000002 | 4 | 2.000000 | 0.0184411 | -7.8761116 | -7.7357386 | -7.8791975 | -7.8196798 |
| USDCHF | eGARCH | 0.0000001 | 4 | 2.000000 | 0.0194239 | -7.9009921 | -7.7880089 | -7.9030600 | -7.8555713 |
| USDCHF | gjrGARCH | 0.0000003 | 4 | 2.000000 | 0.0176093 | -7.8932971 | -7.7803140 | -7.8953651 | -7.8478764 |
| USDCHF | apARCH | 0.0000002 | 4 | 2.000000 | 0.0175526 | -7.8837665 | -7.7570884 | -7.8863176 | -7.8328402 |
| USDCHF | iGARCH | 0.0000003 | 4 | 2.000000 | 0.0198707 | -7.8801376 | -7.7945442 | -7.8813971 | -7.8457279 |
| USDCHF | csGARCH | 0.0000001 | 4 | 2.000000 | 0.0201152 | -7.8635773 | -7.7368992 | -7.8661284 | -7.8126510 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 0.0000000 | 4 | 2.000000 | 0.0049855 | -8.2818931 | -8.2069851 | -8.2827573 | -8.2517860 |
| USDCAD | fGARCH.GARCH | 0.0000000 | 4 | 2.000000 | 0.0049738 | -8.2817294 | -8.2068214 | -8.2825936 | -8.2516222 |
| USDCAD | fGARCH.TGARCH | 0.0000000 | 4 | 2.000000 | 0.0051920 | -8.2981108 | -8.2095831 | -8.2993091 | -8.2625296 |
| USDCAD | fGARCH.AVGARCH | 0.0000000 | 4 | 2.000000 | 0.0929052 | -8.1148285 | -8.0126812 | -8.1164139 | -8.0737733 |
| USDCAD | fGARCH.NGARCH | 0.0000000 | 4 | 2.000000 | 0.0048273 | -8.2735840 | -8.1850564 | -8.2747824 | -8.2380029 |
| USDCAD | fGARCH.NAGARCH | 0.0000000 | 4 | 2.000000 | 0.0037520 | -8.2868248 | -8.1982972 | -8.2880231 | -8.2512436 |
| USDCAD | fGARCH.APARCH | 0.0000000 | 4 | 2.000000 | 0.0508286 | -8.1477858 | -8.0456386 | -8.1493712 | -8.1067306 |
| USDCAD | fGARCH.GJRGARCH | 0.0000000 | 4 | 2.000000 | 0.0032447 | -8.2888576 | -8.2003299 | -8.2900559 | -8.2532764 |
| USDCAD | fGARCH.ALLGARCH | 0.0000001 | 4 | 2.000000 | 0.0040514 | -8.2748314 | -8.1590645 | -8.2768561 | -8.2283022 |
| USDCAD | eGARCH | 0.0000001 | 4 | 2.000000 | 0.0050232 | -8.2940264 | -8.2054988 | -8.2952247 | -8.2584452 |
| USDCAD | gjrGARCH | 0.0000000 | 4 | 2.000000 | 0.0032165 | -8.2887046 | -8.2001769 | -8.2899029 | -8.2531234 |
| USDCAD | apARCH | 0.0000000 | 4 | 2.000000 | 0.0037201 | -8.2824580 | -8.1803107 | -8.2840434 | -8.2414028 |
| USDCAD | iGARCH | 0.0000000 | 4 | 2.000000 | 0.0046769 | -8.2861995 | -8.2249111 | -8.2867831 | -8.2615663 |
| USDCAD | csGARCH | 0.0000000 | 4 | 2.000000 | 0.0049357 | -8.2689115 | -8.1667643 | -8.2704970 | -8.2278563 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 0.0000005 | 4 | 2.000000 | 0.0055601 | -6.9273647 | -6.8356839 | -6.9286566 | -6.8905204 |
| USDCNY | fGARCH.GARCH | 0.0000005 | 4 | 2.000000 | 0.0055601 | -6.9273648 | -6.8356840 | -6.9286567 | -6.8905205 |
| USDCNY | fGARCH.TGARCH | 0.0000008 | 4 | 2.000000 | 0.0048566 | -6.8925111 | -6.7872481 | -6.8942002 | -6.8502084 |
| USDCNY | fGARCH.AVGARCH | 0.0000005 | 4 | 2.000000 | 0.0111231 | -6.9095713 | -6.7907259 | -6.9117090 | -6.8618102 |
| USDCNY | fGARCH.NGARCH | 0.0000004 | 4 | 2.000000 | 0.0048438 | -6.9226063 | -6.8173432 | -6.9242953 | -6.8803036 |
| USDCNY | fGARCH.NAGARCH | 0.0000005 | 4 | 2.000000 | 0.0050575 | -6.9179916 | -6.8127285 | -6.9196806 | -6.8756888 |
| USDCNY | fGARCH.APARCH | 0.0000004 | 4 | 2.000000 | 0.0048932 | -6.9185218 | -6.7996764 | -6.9206595 | -6.8707607 |
| USDCNY | fGARCH.GJRGARCH | 0.0000005 | 4 | 2.000000 | 0.0049980 | -6.9182496 | -6.8129865 | -6.9199386 | -6.8759469 |
| USDCNY | fGARCH.ALLGARCH | 0.0000006 | 4 | 2.000000 | 0.0049341 | -6.9226321 | -6.7902043 | -6.9252692 | -6.8694125 |
| USDCNY | eGARCH | 0.0000004 | 4 | 2.000000 | 0.0044761 | -6.8891119 | -6.7838488 | -6.8908009 | -6.8468092 |
| USDCNY | gjrGARCH | 0.0000005 | 4 | 2.000000 | 0.0049979 | -6.9182497 | -6.8129866 | -6.9199387 | -6.8759470 |
| USDCNY | apARCH | 0.0000004 | 4 | 2.000000 | 0.0050421 | -6.9182851 | -6.7994396 | -6.9204227 | -6.8705239 |
| USDCNY | iGARCH | 0.0000006 | 4 | 2.000000 | 0.0051785 | -6.9005154 | -6.8224169 | -6.9014626 | -6.8691295 |
| USDCNY | csGARCH | 0.0000005 | 4 | 2.000000 | 0.0055494 | -6.9114237 | -6.7925783 | -6.9135614 | -6.8636626 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 0.0043414 | 4 | 1.997829 | 0.0272442 | 0.8165514 | 0.9014410 | 0.8154383 | 0.8506665 |
| USDJPY | fGARCH.GARCH | 0.0043414 | 4 | 1.997829 | 0.0272442 | 0.8165514 | 0.9014410 | 0.8154383 | 0.8506665 |
| USDJPY | fGARCH.TGARCH | 0.0042872 | 4 | 1.997856 | 0.0280165 | 0.7848311 | 0.8833030 | 0.7833470 | 0.8244046 |
| USDJPY | fGARCH.AVGARCH | 0.0043247 | 4 | 1.997838 | 0.0250116 | 0.7776130 | 0.8896673 | 0.7757060 | 0.8226450 |
| USDJPY | fGARCH.NGARCH | 0.0043057 | 4 | 1.997847 | 0.0311397 | 0.8114503 | 0.9099222 | 0.8099662 | 0.8510238 |
| USDJPY | fGARCH.NAGARCH | 0.0048188 | 4 | 1.997591 | 0.0260458 | 0.7715537 | 0.8700256 | 0.7700696 | 0.8111272 |
| USDJPY | fGARCH.APARCH | 0.0045436 | 4 | 1.997728 | 0.0297432 | 0.7888246 | 0.9008789 | 0.7869176 | 0.8338565 |
| USDJPY | fGARCH.GJRGARCH | 0.0043442 | 4 | 1.997828 | 0.0268770 | 0.7971652 | 0.8956372 | 0.7956812 | 0.8367387 |
| USDJPY | fGARCH.ALLGARCH | 0.0019024 | 4 | 1.999049 | 0.0263061 | 0.7644200 | 0.8900566 | 0.7620388 | 0.8149104 |
| USDJPY | eGARCH | 0.0041875 | 4 | 1.997906 | 0.0278439 | 0.7416013 | 0.8400733 | 0.7401173 | 0.7811748 |
| USDJPY | gjrGARCH | 0.0047415 | 4 | 1.997629 | 0.0263785 | 0.7701763 | 0.8686482 | 0.7686922 | 0.8097498 |
| USDJPY | apARCH | 0.0051226 | 4 | 1.997439 | 0.0298260 | 0.7886781 | 0.9007324 | 0.7867711 | 0.8337100 |
| USDJPY | iGARCH | 0.0043089 | 4 | 1.997845 | 0.0271791 | 0.8196221 | 0.8909294 | 0.8188273 | 0.8482788 |
| USDJPY | csGARCH | 0.0042846 | 4 | 1.997858 | 0.0272044 | 0.8340534 | 0.9461076 | 0.8321463 | 0.8790853 |
6.1.1.3A : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 0.0006203 | 28 | 0.2856700 | 9.713449 | -6.628971 | -6.543381 | -6.630156 | -6.594571 |
| fGARCH.GARCH | 0.0006203 | 28 | 0.2856700 | 9.713274 | -6.628914 | -6.543324 | -6.630099 | -6.594514 |
| fGARCH.TGARCH | 0.0006126 | 28 | 0.2856705 | 9.486882 | -6.604057 | -6.504853 | -6.605616 | -6.564185 |
| fGARCH.AVGARCH | 0.0006179 | 28 | 0.2856701 | 9.383348 | -6.592463 | -6.479644 | -6.594449 | -6.547119 |
| fGARCH.NGARCH | 0.0006152 | 28 | 0.2856703 | 9.695058 | -6.655243 | -6.556039 | -6.656803 | -6.615371 |
| fGARCH.NAGARCH | 0.0006885 | 28 | 0.2856651 | 9.760064 | -6.700955 | -6.601751 | -6.702515 | -6.661083 |
| fGARCH.APARCH | 0.0006492 | 28 | 0.2856679 | 9.572200 | -6.624296 | -6.511477 | -6.626283 | -6.578952 |
| fGARCH.GJRGARCH | 0.0006207 | 28 | 0.2856700 | 9.687413 | -6.637586 | -6.538382 | -6.639145 | -6.597714 |
| fGARCH.ALLGARCH | 0.0002719 | 28 | 0.2856949 | 9.726224 | -6.713123 | -6.586690 | -6.715588 | -6.662307 |
| eGARCH | 0.0005983 | 28 | 0.2856716 | 9.767911 | -6.755209 | -6.656004 | -6.756768 | -6.715337 |
| gjrGARCH | 0.0006775 | 28 | 0.2856659 | 9.760039 | -6.694914 | -6.595710 | -6.696474 | -6.655042 |
| apARCH | 0.0007319 | 28 | 0.2856620 | 9.665221 | -6.665568 | -6.552750 | -6.667555 | -6.620224 |
| iGARCH | 0.0006157 | 28 | 0.2856703 | 9.714553 | -6.626525 | -6.554550 | -6.627388 | -6.597597 |
| csGARCH | 0.0006122 | 28 | 0.2856706 | 9.858674 | -6.708993 | -6.596175 | -6.710980 | -6.663650 |
6.1.1.3B : Table summary
Now I select 9 models which almost run all data from 2013-01-01 to 2017-08-30. More observations will be able to know the best model. The models includes :
## filter gmds
gmds2 <- c('sGARCH', 'fGARCH.GARCH', 'fGARCH.TGARCH', 'fGARCH.NGARCH', 'fGARCH.NAGARCH', 'fGARCH.GJRGARCH', 'gjrGARCH', 'iGARCH', 'csGARCH')
## check completed dataset.
mdate <- fx %>% dplyr::filter(Model %in% gmds2) %>%
dplyr::count(Date, Model)
##filter 7 currency and OHLC data.
united.dateID <- mdate %>% dplyr::filter(n == 28) %>% .$Date %>% unique
united.fx <- fx %>% dplyr::filter(Model %in% gmds2 & Date %in% united.dateID) %>%
mutate(Model = factor(Model))
## filter all predictive error where sd >= 20%.
notID <- united.fx %>%
mutate(diff = abs(Price.T1/Price),
se = ifelse(diff <= 0.8 | diff >= 1.25, 1, 0)) %>%
dplyr::filter(se == 1)
ntimeID <- notID %>% .$Date %>% unique
acc <- united.fx %>% dplyr::filter(!Date %in% ntimeID) %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 0.0000005 | 4461 | 0.0017933 | 0.2699796 | -7.071027 | -6.992053 | -7.072019 | -7.039283 |
| USDAUD | fGARCH.GARCH | 0.0000005 | 4460 | 0.0017937 | 0.2694188 | -7.070081 | -6.991120 | -7.071073 | -7.038342 |
| USDAUD | fGARCH.TGARCH | 0.0000026 | 4416 | 0.0018116 | 0.5514574 | -6.880359 | -6.787762 | -6.881701 | -6.843140 |
| USDAUD | fGARCH.NGARCH | 0.0000040 | 4400 | 0.0018182 | 4356.0994977 | -14.985021 | -14.892392 | -14.986365 | -14.947789 |
| USDAUD | fGARCH.NAGARCH | 0.0000011 | 3804 | 0.0021030 | 15.8511697 | -7.118149 | -7.024525 | -7.119521 | -7.080516 |
| USDAUD | fGARCH.GJRGARCH | 0.0000006 | 3048 | 0.0026247 | 0.2601535 | -7.251001 | -7.158796 | -7.252334 | -7.213938 |
| USDAUD | gjrGARCH | 0.0000010 | 4464 | 0.0017921 | 0.2814564 | -7.073862 | -6.981228 | -7.075206 | -7.036628 |
| USDAUD | iGARCH | 0.0000006 | 4464 | 0.0017921 | 0.2709502 | -7.073407 | -7.008064 | -7.074102 | -7.047142 |
| USDAUD | csGARCH | 0.0000007 | 4444 | 0.0018002 | 0.2718120 | -7.056629 | -6.950314 | -7.058378 | -7.013896 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 0.0000004 | 4464 | 0.0017921 | 0.3023366 | -8.064762 | -7.983548 | -8.065817 | -8.032117 |
| USDEUR | fGARCH.GARCH | 0.0000004 | 4464 | 0.0017921 | 0.3023260 | -8.064753 | -7.983539 | -8.065808 | -8.032108 |
| USDEUR | fGARCH.TGARCH | 0.0000007 | 4172 | 0.0019175 | 0.4659505 | -7.918904 | -7.823735 | -7.920328 | -7.880651 |
| USDEUR | fGARCH.NGARCH | 0.0000017 | 4416 | 0.0018116 | 5095.4300460 | -16.462979 | -16.368339 | -16.464388 | -16.424938 |
| USDEUR | fGARCH.NAGARCH | 0.0000004 | 3708 | 0.0021575 | 18.6673500 | -8.051872 | -7.956069 | -8.053316 | -8.013363 |
| USDEUR | fGARCH.GJRGARCH | 0.0000003 | 4280 | 0.0018692 | 0.3079026 | -8.080946 | -7.985945 | -8.082365 | -8.042760 |
| USDEUR | gjrGARCH | 0.0000003 | 4464 | 0.0017921 | 0.3119642 | -8.082523 | -7.987663 | -8.083938 | -8.044394 |
| USDEUR | iGARCH | 0.0000004 | 4464 | 0.0017921 | 0.3048671 | -8.058280 | -7.990712 | -8.059030 | -8.031121 |
| USDEUR | csGARCH | 0.0000023 | 4464 | 0.0017921 | 0.2972484 | -8.049892 | -7.941386 | -8.051719 | -8.006277 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 0.0000007 | 4464 | 0.0017921 | 0.4157590 | -8.595094 | -8.511833 | -8.596216 | -8.561629 |
| USDGBP | fGARCH.GARCH | 0.0000007 | 4460 | 0.0017937 | 0.4155566 | -8.594499 | -8.511268 | -8.595621 | -8.561046 |
| USDGBP | fGARCH.TGARCH | 0.0000008 | 4408 | 0.0018149 | 0.6550242 | -8.373232 | -8.276292 | -8.374721 | -8.334268 |
| USDGBP | fGARCH.NGARCH | 0.0000016 | 4408 | 0.0018149 | 3597.2568704 | -14.245800 | -14.148806 | -14.247292 | -14.206815 |
| USDGBP | fGARCH.NAGARCH | 0.0000005 | 4196 | 0.0019066 | 54.0487066 | -8.315425 | -8.219126 | -8.316896 | -8.276719 |
| USDGBP | fGARCH.GJRGARCH | 0.0000007 | 4436 | 0.0018034 | 0.4135185 | -8.609744 | -8.512850 | -8.611232 | -8.570799 |
| USDGBP | gjrGARCH | 0.0000008 | 4464 | 0.0017921 | 0.4135018 | -8.620635 | -8.523745 | -8.622123 | -8.581692 |
| USDGBP | iGARCH | 0.0000009 | 4464 | 0.0017921 | 0.4150226 | -8.595377 | -8.525746 | -8.596186 | -8.567390 |
| USDGBP | csGARCH | 0.0000009 | 4464 | 0.0017921 | 0.4048251 | -8.581658 | -8.471138 | -8.583565 | -8.537236 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 0.0000027 | 4460 | 0.0017937 | 0.3029619 | -7.604226 | -7.524247 | -7.605248 | -7.572078 |
| USDCHF | fGARCH.GARCH | 0.0000027 | 4464 | 0.0017921 | 0.3031340 | -7.604124 | -7.524143 | -7.605146 | -7.571975 |
| USDCHF | fGARCH.TGARCH | 0.0000016 | 4332 | 0.0018467 | 0.4023516 | -7.523015 | -7.429198 | -7.524397 | -7.485305 |
| USDCHF | fGARCH.NGARCH | 0.0000022 | 4420 | 0.0018100 | 3745.0131388 | -14.256352 | -14.162608 | -14.257733 | -14.218671 |
| USDCHF | fGARCH.NAGARCH | 0.0000021 | 3100 | 0.0025806 | 104.3225056 | -7.003817 | -6.909794 | -7.005204 | -6.966023 |
| USDCHF | fGARCH.GJRGARCH | 0.0000017 | 4308 | 0.0018570 | 0.2851070 | -7.623143 | -7.529389 | -7.624524 | -7.585458 |
| USDCHF | gjrGARCH | 0.0000019 | 4464 | 0.0017921 | 0.2858777 | -7.642784 | -7.549156 | -7.644161 | -7.605150 |
| USDCHF | iGARCH | 0.0000364 | 4464 | 0.0017921 | 0.4002800 | -7.551245 | -7.484911 | -7.551966 | -7.524581 |
| USDCHF | csGARCH | 0.0000112 | 4460 | 0.0017937 | 0.3124774 | -7.581463 | -7.474190 | -7.583247 | -7.538344 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 0.0000009 | 4464 | 0.0017921 | 0.3530811 | -7.669945 | -7.588025 | -7.671029 | -7.637017 |
| USDCAD | fGARCH.GARCH | 0.0000009 | 4464 | 0.0017921 | 0.3532523 | -7.669886 | -7.587965 | -7.670969 | -7.636957 |
| USDCAD | fGARCH.TGARCH | 0.0000019 | 4340 | 0.0018433 | 0.6889671 | -7.449413 | -7.353718 | -7.450863 | -7.410948 |
| USDCAD | fGARCH.NGARCH | 0.0000060 | 4392 | 0.0018215 | 5600.0436718 | -18.032121 | -17.936461 | -18.033569 | -17.993670 |
| USDCAD | fGARCH.NAGARCH | 0.0000004 | 4148 | 0.0019286 | 3.1700289 | -7.686479 | -7.591025 | -7.687921 | -7.648111 |
| USDCAD | fGARCH.GJRGARCH | 0.0000010 | 4380 | 0.0018265 | 0.3591763 | -7.677804 | -7.582210 | -7.679250 | -7.639379 |
| USDCAD | gjrGARCH | 0.0000015 | 4464 | 0.0017921 | 0.3584443 | -7.674606 | -7.579037 | -7.676052 | -7.636192 |
| USDCAD | iGARCH | 0.0000007 | 4464 | 0.0017921 | 0.3549423 | -7.668798 | -7.600526 | -7.669573 | -7.641355 |
| USDCAD | csGARCH | 0.0000005 | 4448 | 0.0017986 | 0.3522245 | -7.655085 | -7.545843 | -7.656946 | -7.611174 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 0.0003905 | 4460 | 0.0017935 | 1.0777407 | -6.154664 | -6.065816 | -6.155908 | -6.118951 |
| USDCNY | fGARCH.GARCH | 0.0002715 | 4460 | 0.0017936 | 1.0779078 | -6.154620 | -6.065766 | -6.155865 | -6.118906 |
| USDCNY | fGARCH.TGARCH | 0.0010647 | 4384 | 0.0018243 | 5.6981749 | -5.861576 | -5.759146 | -5.863207 | -5.820405 |
| USDCNY | fGARCH.NGARCH | 0.0008949 | 4416 | 0.0018112 | 3397.9158176 | -13.148282 | -13.045917 | -13.149912 | -13.107137 |
| USDCNY | fGARCH.NAGARCH | 0.0001924 | 4344 | 0.0018415 | 14.6909311 | -6.021741 | -5.919184 | -6.023377 | -5.980519 |
| USDCNY | fGARCH.GJRGARCH | 0.0003191 | 3292 | 0.0024299 | 0.9990384 | -6.462816 | -6.359577 | -6.464473 | -6.421319 |
| USDCNY | gjrGARCH | 0.0002957 | 4456 | 0.0017952 | 1.1384250 | -6.195814 | -6.093322 | -6.197448 | -6.154618 |
| USDCNY | iGARCH | 0.0004560 | 4464 | 0.0017919 | 1.2247766 | -6.082914 | -6.007713 | -6.083823 | -6.052688 |
| USDCNY | csGARCH | 0.0005634 | 4464 | 0.0017919 | 1.2115806 | -6.126681 | -6.010566 | -6.128755 | -6.080009 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 0.0095842 | 4464 | 0.0017878 | 0.2083023 | 1.850203 | 1.935079 | 1.849036 | 1.884318 |
| USDJPY | fGARCH.GARCH | 0.0096108 | 4464 | 0.0017878 | 0.2078274 | 1.850140 | 1.935017 | 1.848973 | 1.884256 |
| USDJPY | fGARCH.TGARCH | 0.0104237 | 4456 | 0.0017907 | 0.2222811 | 1.857992 | 1.956475 | 1.856452 | 1.897576 |
| USDJPY | fGARCH.NGARCH | 0.0398521 | 4396 | 0.0018017 | 4704.0555629 | -7.250098 | -7.151581 | -7.251638 | -7.210500 |
| USDJPY | fGARCH.NAGARCH | 0.0071257 | 4368 | 0.0018282 | 0.2147368 | 1.830910 | 1.929323 | 1.829373 | 1.870467 |
| USDJPY | fGARCH.GJRGARCH | 0.0080632 | 4416 | 0.0018079 | 0.2112268 | 1.842797 | 1.941390 | 1.841254 | 1.882426 |
| USDJPY | gjrGARCH | 0.0077127 | 4464 | 0.0017887 | 0.2156022 | 1.839639 | 1.938153 | 1.838099 | 1.879236 |
| USDJPY | iGARCH | 0.0096285 | 4464 | 0.0017878 | 0.2123364 | 1.852977 | 1.924215 | 1.852130 | 1.881611 |
| USDJPY | csGARCH | 0.0111032 | 4464 | 0.0017871 | 0.2072699 | 1.859822 | 1.971974 | 1.857856 | 1.904901 |
6.1.2.1A : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 0.0014261 | 31237 | 0.0002560 | 11.69528 | -6.186811 | -6.104087 | -6.187910 | -6.153560 |
| fGARCH.GARCH | 0.0014130 | 31236 | 0.0002560 | 11.69416 | -6.186414 | -6.103695 | -6.187513 | -6.153166 |
| fGARCH.TGARCH | 0.0016766 | 30508 | 0.0002621 | 12.32388 | -5.987565 | -5.891102 | -5.989031 | -5.948792 |
| fGARCH.NGARCH | 0.0058095 | 30848 | 0.0002590 | 4365.40313 | -14.055190 | -13.958825 | -14.056653 | -14.016456 |
| fGARCH.NAGARCH | 0.0011557 | 27668 | 0.0002891 | 39.14422 | -5.912306 | -5.815506 | -5.913782 | -5.873398 |
| fGARCH.GJRGARCH | 0.0013024 | 28160 | 0.0002840 | 12.76315 | -6.196286 | -6.099861 | -6.197752 | -6.157528 |
| gjrGARCH | 0.0011450 | 31240 | 0.0002560 | 11.72611 | -6.207230 | -6.110861 | -6.208693 | -6.168495 |
| iGARCH | 0.0014462 | 31248 | 0.0002559 | 11.71105 | -6.168149 | -6.099065 | -6.168936 | -6.140381 |
| csGARCH | 0.0016710 | 31208 | 0.0002562 | 11.70860 | -6.168716 | -6.058696 | -6.170598 | -6.124494 |
6.1.2.1B : Table summary
| Model | n |
|---|---|
| sGARCH | 2 |
| fGARCH.GARCH | 5 |
| fGARCH.TGARCH | 5 |
| fGARCH.NGARCH | 74 |
| fGARCH.NAGARCH | 14 |
| fGARCH.GJRGARCH | 4 |
| gjrGARCH | 3 |
| iGARCH | 10 |
| csGARCH | 5 |
6.1.2.1C : Table summary
| .id | Model | Date | Type | Price | Price.T1 | Akaike | Bayes | Shibata | Hannan.Quinn | diff | se |
|---|---|---|---|---|---|---|---|---|---|---|---|
| USDAUD | fGARCH.TGARCH | 2013-06-03 | USDAUD.Op | 1.02600 | -7.365624e+01 | 24.941247 | 25.064162 | 24.938973 | 24.990655 | 7.178971e+01 | 1 |
| USDAUD | fGARCH.NGARCH | 2013-06-27 | USDAUD.Lo | 1.07700 | 2.542027e+00 | -590.320340 | -590.197426 | -590.322615 | -590.270933 | 2.360285e+00 | 1 |
| USDAUD | fGARCH.NGARCH | 2013-08-04 | USDAUD.Op | 1.12300 | 1.260885e+39 | -299.194470 | -299.084911 | -299.196290 | -299.150426 | 1.122783e+39 | 1 |
| USDAUD | fGARCH.NGARCH | 2013-08-04 | USDAUD.Cl | 1.12290 | 9.147871e+10 | 192.689015 | 192.798574 | 192.687195 | 192.733059 | 8.146648e+10 | 1 |
| USDAUD | fGARCH.NGARCH | 2014-04-14 | USDAUD.Op | 1.06200 | 1.419924e+09 | -416.149142 | -416.012570 | -416.151936 | -416.094244 | 1.337028e+09 | 1 |
| USDAUD | fGARCH.NGARCH | 2014-07-24 | USDAUD.Hi | 1.06400 | 2.487249e+34 | -502.592743 | -502.428857 | -502.596729 | -502.526867 | 2.337640e+34 | 1 |
| USDAUD | fGARCH.NGARCH | 2017-03-26 | USDAUD.Lo | 1.30700 | 1.111220e-02 | -586.980288 | -586.857373 | -586.982562 | -586.930880 | 8.502100e-03 | 1 |
| USDAUD | fGARCH.NAGARCH | 2015-02-09 | USDAUD.Op | 1.28800 | 9.042209e+09 | 101.921621 | 102.058192 | 101.918826 | 101.976518 | 7.020349e+09 | 1 |
| USDAUD | fGARCH.NAGARCH | 2015-02-10 | USDAUD.Op | 1.28300 | -9.623617e+31 | 153.814604 | 153.950801 | 153.811831 | 153.869344 | 7.500870e+31 | 1 |
| USDAUD | iGARCH | 2014-10-15 | USDAUD.Cl | 1.13730 | 2.310843e+145 | 738.699064 | 738.808021 | 738.697272 | 738.742856 | 2.031868e+145 | 1 |
| USDEUR | fGARCH.GARCH | 2015-02-05 | USDEUR.Hi | 0.88400 | 2.683682e+92 | 412.262447 | 412.385024 | 412.260190 | 412.311713 | 3.035839e+92 | 1 |
| USDEUR | fGARCH.GARCH | 2017-06-18 | USDEUR.Cl | 0.89220 | 6.667688e+68 | 356.680437 | 356.817009 | 356.677643 | 356.735335 | 7.473311e+68 | 1 |
| USDEUR | fGARCH.NGARCH | 2014-10-14 | USDEUR.Lo | 0.77900 | -2.018651e+51 | -468.909622 | -468.759806 | -468.912961 | -468.849407 | 2.591336e+51 | 1 |
| USDEUR | fGARCH.NGARCH | 2015-03-02 | USDEUR.Lo | 0.89000 | -4.015994e+07 | 83.346290 | 83.510176 | 83.342305 | 83.412167 | 4.512353e+07 | 1 |
| USDEUR | fGARCH.NGARCH | 2015-06-04 | USDEUR.Lo | 0.88700 | -1.394863e+18 | -545.380537 | -545.244340 | -545.383310 | -545.325796 | 1.572562e+18 | 1 |
| USDEUR | fGARCH.NGARCH | 2015-06-24 | USDEUR.Lo | 0.89100 | 1.892803e+10 | 77.586765 | 77.722962 | 77.583992 | 77.641506 | 2.124358e+10 | 1 |
| USDGBP | fGARCH.TGARCH | 2014-06-19 | USDGBP.Lo | 0.58600 | -3.465523e+73 | 364.832355 | 365.037213 | 364.826216 | 364.914701 | 5.913861e+73 | 1 |
| USDGBP | fGARCH.NGARCH | 2014-03-31 | USDGBP.Cl | 0.60001 | -1.642110e+04 | -444.661563 | -444.524991 | -444.664357 | -444.606666 | 2.736805e+04 | 1 |
| USDGBP | fGARCH.NGARCH | 2014-05-01 | USDGBP.Cl | 0.59188 | 9.637298e-01 | -516.051131 | -515.914560 | -516.053925 | -515.996234 | 1.628252e+00 | 1 |
| USDGBP | fGARCH.NGARCH | 2014-06-19 | USDGBP.Lo | 0.58600 | 4.316118e-01 | -160.018385 | -159.813528 | -160.024525 | -159.936039 | 7.365389e-01 | 1 |
| USDGBP | fGARCH.NGARCH | 2015-04-16 | USDGBP.Cl | 0.67016 | 1.865748e+15 | -556.647438 | -556.511242 | -556.650211 | -556.592698 | 2.784033e+15 | 1 |
| USDGBP | fGARCH.NGARCH | 2015-04-21 | USDGBP.Op | 0.67000 | -1.002521e+06 | -574.983967 | -574.847770 | -574.986740 | -574.929227 | 1.496300e+06 | 1 |
| USDGBP | fGARCH.NGARCH | 2015-06-08 | USDGBP.Op | 0.65200 | 5.022905e+36 | -490.210255 | -490.087678 | -490.212512 | -490.160989 | 7.703841e+36 | 1 |
| USDGBP | fGARCH.NGARCH | 2015-06-16 | USDGBP.Op | 0.63900 | 1.392346e+72 | 349.939882 | 350.048839 | 349.938090 | 349.983675 | 2.178945e+72 | 1 |
| USDGBP | fGARCH.NGARCH | 2016-07-19 | USDGBP.Cl | 0.76287 | -6.365327e+09 | 114.898499 | 115.034323 | 114.895747 | 114.953084 | 8.343921e+09 | 1 |
| USDGBP | fGARCH.NGARCH | 2016-07-20 | USDGBP.Hi | 0.75900 | 7.366569e+74 | -405.810489 | -405.701830 | -405.812268 | -405.766822 | 9.705624e+74 | 1 |
| USDGBP | csGARCH | 2014-12-05 | USDGBP.Lo | 0.63700 | 9.285102e+149 | 758.957433 | 759.107249 | 758.954093 | 759.017647 | 1.457630e+150 | 1 |
| USDCHF | sGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.189676e+00 | -6.687989 | -6.606271 | -6.689007 | -6.655145 | 1.399619e+00 | 1 |
| USDCHF | fGARCH.GARCH | 2014-05-25 | USDCHF.Hi | 0.89700 | -3.484066e+62 | 366.067877 | 366.273301 | 366.061692 | 366.150461 | 3.884132e+62 | 1 |
| USDCHF | fGARCH.GARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.189676e+00 | -6.687989 | -6.606271 | -6.689007 | -6.655145 | 1.399619e+00 | 1 |
| USDCHF | fGARCH.TGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.182560e+00 | -6.882116 | -6.786779 | -6.883495 | -6.843798 | 1.391247e+00 | 1 |
| USDCHF | fGARCH.NGARCH | 2013-12-12 | USDCHF.Op | 0.88700 | -3.879205e+00 | -432.539483 | -432.402912 | -432.542277 | -432.484586 | 4.373400e+00 | 1 |
| USDCHF | fGARCH.NGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.182556e+00 | -6.811955 | -6.716617 | -6.813334 | -6.773637 | 1.391243e+00 | 1 |
| USDCHF | fGARCH.NGARCH | 2015-09-07 | USDCHF.Lo | 0.97000 | -8.823318e+01 | -587.029347 | -586.920390 | -587.031140 | -586.985555 | 9.096204e+01 | 1 |
| USDCHF | fGARCH.NGARCH | 2015-10-30 | USDCHF.Hi | 0.99100 | -1.889325e+01 | -584.267632 | -584.158374 | -584.269437 | -584.223714 | 1.906483e+01 | 1 |
| USDCHF | fGARCH.NAGARCH | 2013-12-05 | USDCHF.Op | 0.90200 | 4.359195e+145 | 731.450007 | 731.586578 | 731.447212 | 731.504904 | 4.832810e+145 | 1 |
| USDCHF | fGARCH.NAGARCH | 2013-12-16 | USDCHF.Op | 0.89000 | 2.195181e+145 | 732.215372 | 732.352321 | 732.212557 | 732.270427 | 2.466495e+145 | 1 |
| USDCHF | fGARCH.NAGARCH | 2015-01-09 | USDCHF.Op | 1.01800 | -1.228938e+24 | 226.375920 | 226.539355 | 226.371964 | 226.441608 | 1.207208e+24 | 1 |
| USDCHF | fGARCH.NAGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.188451e+00 | -6.758750 | -6.663413 | -6.760129 | -6.720432 | 1.398178e+00 | 1 |
| USDCHF | fGARCH.GJRGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.189203e+00 | -6.775060 | -6.679723 | -6.776439 | -6.736742 | 1.399062e+00 | 1 |
| USDCHF | gjrGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.187461e+00 | -6.834457 | -6.739119 | -6.835835 | -6.796138 | 1.397013e+00 | 1 |
| USDCHF | gjrGARCH | 2015-01-19 | USDCHF.Lo | 0.85700 | 5.503465e-01 | -6.799206 | -6.703606 | -6.800595 | -6.760778 | 6.421780e-01 | 1 |
| USDCHF | iGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.189656e+00 | -6.696311 | -6.628212 | -6.697021 | -6.668940 | 1.399595e+00 | 1 |
| USDCHF | iGARCH | 2015-01-19 | USDCHF.Lo | 0.85700 | 5.467194e-01 | -6.659730 | -6.591444 | -6.660445 | -6.632281 | 6.379457e-01 | 1 |
| USDCHF | iGARCH | 2015-01-20 | USDCHF.Lo | 0.86900 | 1.169574e+00 | -6.632037 | -6.563939 | -6.632748 | -6.604667 | 1.345885e+00 | 1 |
| USDCHF | iGARCH | 2015-01-21 | USDCHF.Lo | 0.85100 | 5.536845e-01 | -6.599117 | -6.531019 | -6.599827 | -6.571747 | 6.506281e-01 | 1 |
| USDCHF | iGARCH | 2015-01-22 | USDCHF.Lo | 0.85300 | 1.132264e+00 | -6.569994 | -6.501896 | -6.570705 | -6.542624 | 1.327390e+00 | 1 |
| USDCHF | iGARCH | 2015-01-26 | USDCHF.Lo | 0.87600 | 1.153558e+00 | -6.519110 | -6.450824 | -6.519825 | -6.491661 | 1.316847e+00 | 1 |
| USDCHF | iGARCH | 2015-01-27 | USDCHF.Lo | 0.89400 | 6.896106e-01 | -6.470927 | -6.402829 | -6.471637 | -6.443557 | 7.713765e-01 | 1 |
| USDCHF | iGARCH | 2015-02-02 | USDCHF.Lo | 0.92000 | 7.319616e-01 | -6.350835 | -6.255235 | -6.352225 | -6.312407 | 7.956105e-01 | 1 |
| USDCHF | csGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.193636e+00 | -6.688153 | -6.579196 | -6.689945 | -6.644361 | 1.404278e+00 | 1 |
| USDCHF | csGARCH | 2015-01-22 | USDCHF.Lo | 0.85300 | 1.141360e+00 | -6.534724 | -6.425767 | -6.536516 | -6.490932 | 1.338054e+00 | 1 |
| USDCHF | csGARCH | 2015-01-23 | USDCHF.Lo | 0.86800 | 6.200740e-01 | -6.493151 | -6.384194 | -6.494943 | -6.449359 | 7.143710e-01 | 1 |
| USDCAD | fGARCH.NGARCH | 2015-02-05 | USDCAD.Hi | 1.25800 | -2.752758e+42 | -487.602382 | -487.425326 | -487.607002 | -487.531219 | 2.188202e+42 | 1 |
| USDCAD | fGARCH.NGARCH | 2015-02-09 | USDCAD.Cl | 1.25170 | -7.979335e+22 | 142.673774 | 142.783031 | 142.671968 | 142.717692 | 6.374798e+22 | 1 |
| USDCAD | fGARCH.NGARCH | 2015-03-29 | USDCAD.Hi | 1.27000 | -6.542943e+22 | -529.240306 | -529.131049 | -529.242112 | -529.196389 | 5.151924e+22 | 1 |
| USDCAD | fGARCH.NGARCH | 2015-07-21 | USDCAD.Hi | 1.30500 | 4.139802e+61 | -435.142670 | -435.006474 | -435.145443 | -435.087930 | 3.172262e+61 | 1 |
| USDCAD | fGARCH.NGARCH | 2016-05-01 | USDCAD.Op | 1.25400 | -6.113225e+60 | -292.286659 | -292.081235 | -292.292844 | -292.204076 | 4.874980e+60 | 1 |
| USDCAD | fGARCH.NGARCH | 2016-05-02 | USDCAD.Hi | 1.27000 | 2.847428e+37 | -493.891329 | -493.741100 | -493.894693 | -493.830942 | 2.242069e+37 | 1 |
| USDCNY | sGARCH | 2014-07-10 | USDCNY.Lo | 2.20100 | 2.987751e+00 | -4.665480 | -4.583537 | -4.666505 | -4.632541 | 1.357452e+00 | 1 |
| USDCNY | fGARCH.GARCH | 2014-07-10 | USDCNY.Lo | 2.20100 | 2.987874e+00 | -4.665479 | -4.583536 | -4.666505 | -4.632541 | 1.357508e+00 | 1 |
| USDCNY | fGARCH.TGARCH | 2013-10-09 | USDCNY.Op | 6.11100 | 5.483283e+03 | 60.013013 | 60.135928 | 60.010739 | 60.062421 | 8.972808e+02 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-17 | USDCNY.Lo | 6.19200 | -3.142299e+01 | -584.776350 | -584.694407 | -584.777376 | -584.743412 | 5.074772e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-20 | USDCNY.Lo | 6.19500 | 1.601180e+01 | -588.464869 | -588.382700 | -588.465903 | -588.431836 | 2.584633e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-21 | USDCNY.Lo | 6.19300 | 1.802707e+02 | -584.204328 | -584.122385 | -584.205354 | -584.171390 | 2.910878e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-22 | USDCNY.Lo | 6.18900 | 6.023818e+01 | -586.383515 | -586.301572 | -586.384541 | -586.350577 | 9.733103e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-23 | USDCNY.Lo | 6.18200 | 1.116223e+02 | -582.294731 | -582.212788 | -582.295756 | -582.261792 | 1.805601e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-27 | USDCNY.Lo | 6.17600 | 4.872521e+01 | -587.187420 | -587.105250 | -587.188453 | -587.154387 | 7.889444e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-31 | USDCNY.Lo | 6.16300 | -1.151893e+02 | -587.546128 | -587.464185 | -587.547153 | -587.513189 | 1.869046e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-03 | USDCNY.Lo | 6.16800 | -1.481046e+00 | -591.735377 | -591.653208 | -591.736411 | -591.702344 | 2.401177e-01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-04 | USDCNY.Lo | 6.16100 | 1.118689e+01 | -590.853714 | -590.771771 | -590.854740 | -590.820775 | 1.815759e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-05 | USDCNY.Lo | 6.15300 | -5.459669e+01 | -563.148807 | -563.066864 | -563.149833 | -563.115869 | 8.873182e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-06 | USDCNY.Lo | 6.14700 | 2.635122e+01 | -591.728569 | -591.646626 | -591.729595 | -591.695631 | 4.286842e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-10 | USDCNY.Lo | 6.14400 | 5.336958e+01 | -588.785684 | -588.703514 | -588.786717 | -588.752651 | 8.686456e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-13 | USDCNY.Lo | 6.14200 | 4.004231e+02 | -583.022533 | -582.940590 | -583.023559 | -582.989595 | 6.519425e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-14 | USDCNY.Lo | 6.13600 | 4.872331e+01 | -586.351874 | -586.269931 | -586.352899 | -586.318935 | 7.940565e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-18 | USDCNY.Lo | 6.12700 | 4.620441e+00 | -583.267547 | -583.185604 | -583.268572 | -583.234608 | 7.541114e-01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-19 | USDCNY.Lo | 6.13000 | 3.981759e+01 | -587.532975 | -587.451032 | -587.534000 | -587.500036 | 6.495529e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-20 | USDCNY.Lo | 6.13000 | 1.169769e+02 | -586.017467 | -585.935524 | -586.018492 | -585.984528 | 1.908270e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-21 | USDCNY.Lo | 6.14100 | 5.744849e+01 | -586.508501 | -586.426558 | -586.509527 | -586.475563 | 9.354907e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-24 | USDCNY.Lo | 6.14000 | -3.247607e+01 | -589.174302 | -589.092132 | -589.175335 | -589.141269 | 5.289262e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-26 | USDCNY.Lo | 6.13300 | 9.738678e+01 | -587.251542 | -587.169599 | -587.252568 | -587.218604 | 1.587914e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-31 | USDCNY.Lo | 6.12900 | 2.545583e+02 | -584.923023 | -584.840853 | -584.924056 | -584.889989 | 4.153341e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-02 | USDCNY.Lo | 6.13100 | 1.578343e+00 | -590.429012 | -590.347069 | -590.430038 | -590.396074 | 2.574364e-01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-03 | USDCNY.Lo | 6.12500 | 3.759315e+01 | -581.281528 | -581.199585 | -581.282554 | -581.248590 | 6.137657e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-04 | USDCNY.Lo | 6.12800 | -4.565334e+01 | -589.259505 | -589.177562 | -589.260531 | -589.226567 | 7.449958e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-07 | USDCNY.Lo | 6.13000 | 7.649639e+01 | -580.676871 | -580.594702 | -580.677904 | -580.643838 | 1.247902e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-08 | USDCNY.Lo | 6.12200 | -2.517129e+01 | -587.872377 | -587.790434 | -587.873402 | -587.839438 | 4.111612e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-11 | USDCNY.Lo | 6.12000 | -3.251440e+01 | -587.456738 | -587.374795 | -587.457764 | -587.423800 | 5.312810e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-14 | USDCNY.Lo | 6.12500 | -1.796358e+02 | -584.617601 | -584.535431 | -584.618634 | -584.584568 | 2.932830e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-15 | USDCNY.Lo | 6.13200 | -1.112814e+01 | -590.468673 | -590.386730 | -590.469698 | -590.435734 | 1.814765e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-16 | USDCNY.Lo | 6.12900 | -1.759094e+02 | -585.597533 | -585.515590 | -585.598558 | -585.564594 | 2.870116e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-21 | USDCNY.Lo | 6.12800 | -2.039517e+01 | -588.488512 | -588.406343 | -588.489546 | -588.455479 | 3.328194e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-23 | USDCNY.Lo | 6.12400 | 1.512941e+01 | -590.152856 | -590.070913 | -590.153882 | -590.119918 | 2.470511e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-30 | USDCNY.Lo | 6.12800 | 1.553160e+02 | -567.572804 | -567.490861 | -567.573830 | -567.539866 | 2.534531e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-10-01 | USDCNY.Lo | 6.12800 | -1.146657e+02 | -584.091459 | -584.009516 | -584.092485 | -584.058521 | 1.871177e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-10-06 | USDCNY.Lo | 6.12900 | 2.295707e+02 | -583.286508 | -583.204565 | -583.287534 | -583.253570 | 3.745647e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-10-07 | USDCNY.Lo | 6.12500 | 5.146397e+01 | -565.845084 | -565.763141 | -565.846110 | -565.812146 | 8.402281e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-10-09 | USDCNY.Lo | 6.12000 | 6.182692e+01 | -583.758544 | -583.676826 | -583.759562 | -583.725700 | 1.010244e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-11-26 | USDCNY.Lo | 6.12300 | 6.187566e+01 | -583.601907 | -583.520189 | -583.602924 | -583.569062 | 1.010545e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2017-06-15 | USDCNY.Op | 6.80600 | -1.649282e+44 | -461.947546 | -461.824970 | -461.949803 | -461.898280 | 2.423276e+43 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-07-10 | USDCNY.Lo | 2.20100 | 2.977219e+00 | -4.669064 | -4.573464 | -4.670453 | -4.630636 | 1.352666e+00 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-07-24 | USDCNY.Lo | 6.18200 | -3.603032e+02 | 14.561667 | 14.643610 | 14.560642 | 14.594606 | 5.828262e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-07-29 | USDCNY.Lo | 6.16200 | -3.579216e+02 | 14.548624 | 14.630567 | 14.547598 | 14.581562 | 5.808530e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-07-31 | USDCNY.Lo | 6.16300 | -3.531901e+02 | 14.522470 | 14.604413 | 14.521444 | 14.555409 | 5.730814e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-08-04 | USDCNY.Lo | 6.16100 | -3.492923e+02 | 14.548440 | 14.630382 | 14.547414 | 14.581378 | 5.669409e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-08-26 | USDCNY.Lo | 6.13300 | 4.865151e+00 | 104.667516 | 104.749459 | 104.666490 | 104.700454 | 7.932742e-01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-09-04 | USDCNY.Lo | 6.12800 | 4.796821e+02 | 172.167572 | 172.249515 | 172.166546 | 172.200510 | 7.827710e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-10-19 | USDCNY.Lo | 6.11300 | -3.344848e+02 | 98.972743 | 99.054686 | 98.971717 | 99.005682 | 5.471696e+01 | 1 |
| USDCNY | fGARCH.GJRGARCH | 2014-07-10 | USDCNY.Lo | 2.20100 | 2.979918e+00 | -4.677596 | -4.581996 | -4.678985 | -4.639168 | 1.353893e+00 | 1 |
| USDCNY | fGARCH.GJRGARCH | 2014-09-01 | USDCNY.Lo | 6.13200 | 1.263740e+01 | 98.054293 | 98.136236 | 98.053267 | 98.087231 | 2.060893e+00 | 1 |
| USDCNY | fGARCH.GJRGARCH | 2014-11-12 | USDCNY.Lo | 6.11400 | -3.508494e+01 | 94.016565 | 94.098283 | 94.015548 | 94.049410 | 5.738460e+00 | 1 |
| USDCNY | gjrGARCH | 2014-07-10 | USDCNY.Lo | 2.20100 | 2.894085e+00 | -4.702450 | -4.606850 | -4.703839 | -4.664022 | 1.314895e+00 | 1 |
| USDCNY | iGARCH | 2014-07-10 | USDCNY.Lo | 2.20100 | 2.988228e+00 | -4.673441 | -4.605156 | -4.674157 | -4.645993 | 1.357668e+00 | 1 |
| USDCNY | csGARCH | 2014-03-19 | USDCNY.Op | 6.18200 | -4.743008e+149 | 761.606011 | 761.769897 | 761.602025 | 761.671888 | 7.672287e+148 | 1 |
| USDJPY | fGARCH.TGARCH | 2013-03-31 | USDJPY.Op | 94.26200 | -5.215159e+89 | 433.750440 | 433.914326 | 433.746455 | 433.816317 | 5.532621e+87 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-05-20 | USDJPY.Hi | 102.87200 | 1.639729e+20 | 126.895461 | 127.031657 | 126.892687 | 126.950201 | 1.593951e+18 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-06-16 | USDJPY.Hi | 95.10600 | -2.728130e+05 | 179.131969 | 179.268541 | 179.129175 | 179.186867 | 2.868516e+03 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-06-17 | USDJPY.Hi | 95.75300 | 3.511368e+02 | 10.570756 | 10.706952 | 10.567983 | 10.625496 | 3.667111e+00 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-06-19 | USDJPY.Hi | 98.23900 | 4.076553e+124 | 740.361014 | 740.497210 | 740.358240 | 740.415754 | 4.149628e+122 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-07-01 | USDJPY.Hi | 100.43800 | 4.397652e+23 | -244.819452 | -244.683255 | -244.822225 | -244.764711 | 4.378474e+21 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-07-22 | USDJPY.Hi | 100.17000 | -7.099425e+16 | 107.520826 | 107.657022 | 107.518052 | 107.575566 | 7.087376e+14 | 1 |
6.1.2.1D : Table summary
Now I try to filter the dataset again. Below table summarise all dataset which excludes bias but contain OHLC of 7 currencies.
## filter all date which contain OHLC of 7 currencies.
ntimeID2 <- united.fx %>% dplyr::count(Date) %>%
dplyr::filter(n == 252) %>% .$Date #9 models x 7 currencies x OHLC 4 types = 252 observations per day.
united.fx2 <- united.fx %>% dplyr::filter(Date %in% ntimeID2)
## filter all predictive error where sd >= 20%.
notID <- united.fx2 %>%
mutate(diff = abs(Price.T1/Price),
se = ifelse(diff <= 0.8 | diff >= 1.25, 1, 0)) %>%
dplyr::filter(se == 1)
acc <- united.fx2 %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 6.000000e-07 | 2236 | 3.577800e-03 | 0.1625351 | -7.368950 | -7.288749 | -7.369979 | -7.336712 |
| USDAUD | fGARCH.GARCH | 6.000000e-07 | 2236 | 3.577800e-03 | 0.1624570 | -7.368979 | -7.288779 | -7.370009 | -7.336742 |
| USDAUD | fGARCH.TGARCH | 2.494384e+00 | 2236 | 1.346700e-03 | 1.0768079 | -7.120062 | -7.026208 | -7.121447 | -7.082336 |
| USDAUD | fGARCH.NGARCH | 2.766731e+65 | 2236 | -2.474714e+62 | 8326.9953130 | -22.592740 | -22.498886 | -22.594125 | -22.555014 |
| USDAUD | fGARCH.NAGARCH | 4.141950e+60 | 2236 | -3.704785e+57 | 43.6941028 | -7.147520 | -7.053666 | -7.148905 | -7.109794 |
| USDAUD | fGARCH.GJRGARCH | 8.000000e-07 | 2236 | 3.577800e-03 | 0.1693578 | -7.369940 | -7.276086 | -7.371325 | -7.332214 |
| USDAUD | gjrGARCH | 8.000000e-07 | 2236 | 3.577800e-03 | 0.1713696 | -7.376728 | -7.282875 | -7.378113 | -7.339003 |
| USDAUD | iGARCH | 2.388192e+287 | 2236 | -2.136129e+284 | 248.9905666 | -7.037625 | -6.971078 | -7.038352 | -7.010876 |
| USDAUD | csGARCH | 8.000000e-07 | 2236 | 3.577800e-03 | 0.1681670 | -7.351422 | -7.243915 | -7.353216 | -7.308208 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 5.000000e-07 | 2236 | 3.577800e-03 | 0.3248276 | -8.375734 | -8.292899 | -8.376828 | -8.342438 |
| USDEUR | fGARCH.GARCH | 5.000000e-07 | 2236 | 3.577800e-03 | 0.3244428 | -8.375693 | -8.292858 | -8.376787 | -8.342397 |
| USDEUR | fGARCH.TGARCH | 1.100000e-06 | 2236 | 3.577800e-03 | 0.5189860 | -8.230733 | -8.134244 | -8.232193 | -8.191948 |
| USDEUR | fGARCH.NGARCH | 8.701438e+32 | 2236 | -7.783040e+29 | 8706.7409797 | -22.684858 | -22.588369 | -22.686318 | -22.646073 |
| USDEUR | fGARCH.NAGARCH | 4.000000e-07 | 2236 | 3.577800e-03 | 30.6842331 | -8.266987 | -8.170499 | -8.268448 | -8.228203 |
| USDEUR | fGARCH.GJRGARCH | 4.000000e-07 | 2236 | 3.577800e-03 | 0.3266558 | -8.383353 | -8.286864 | -8.384813 | -8.344568 |
| USDEUR | gjrGARCH | 4.000000e-07 | 2236 | 3.577800e-03 | 0.3272131 | -8.399480 | -8.302992 | -8.400941 | -8.360696 |
| USDEUR | iGARCH | 6.000000e-07 | 2236 | 3.577800e-03 | 0.3242069 | -8.374202 | -8.305020 | -8.374983 | -8.346393 |
| USDEUR | csGARCH | 6.000000e-07 | 2236 | 3.577800e-03 | 0.3111112 | -8.360968 | -8.250826 | -8.362847 | -8.316695 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 1.000000e-07 | 2236 | 3.577800e-03 | 0.1141396 | -9.053570 | -8.971985 | -9.054654 | -9.020777 |
| USDGBP | fGARCH.GARCH | 1.000000e-07 | 2236 | 3.577800e-03 | 0.1142206 | -9.053111 | -8.971526 | -9.054195 | -9.020318 |
| USDGBP | fGARCH.TGARCH | 5.371130e+143 | 2236 | -4.804231e+140 | 62.8726733 | -8.613631 | -8.518406 | -8.615076 | -8.575356 |
| USDGBP | fGARCH.NGARCH | 1.128335e+70 | 2236 | -1.009244e+67 | 3668.1035686 | -14.845624 | -14.750400 | -14.847069 | -14.807349 |
| USDGBP | fGARCH.NAGARCH | 1.000000e-07 | 2236 | 3.577800e-03 | 47.7249662 | -8.782240 | -8.687015 | -8.783685 | -8.743965 |
| USDGBP | fGARCH.GJRGARCH | 1.000000e-07 | 2236 | 3.577800e-03 | 0.1173539 | -9.066730 | -8.971505 | -9.068174 | -9.028454 |
| USDGBP | gjrGARCH | 1.000000e-07 | 2236 | 3.577800e-03 | 0.1149523 | -9.079875 | -8.984651 | -9.081320 | -9.041600 |
| USDGBP | iGARCH | 1.000000e-07 | 2236 | 3.577800e-03 | 0.1144318 | -9.053292 | -8.985346 | -9.054069 | -9.025981 |
| USDGBP | csGARCH | 1.000000e-07 | 2236 | 3.577800e-03 | 0.1014799 | -9.038237 | -8.929373 | -9.040095 | -8.994480 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 5.620000e-05 | 2236 | 3.577800e-03 | 0.4628833 | -7.598820 | -7.516889 | -7.599894 | -7.565887 |
| USDCHF | fGARCH.GARCH | 5.630000e-05 | 2236 | 3.577800e-03 | 0.4633472 | -7.598326 | -7.516395 | -7.599400 | -7.565392 |
| USDCHF | fGARCH.TGARCH | 5.200000e-05 | 2236 | 3.577800e-03 | 0.5703948 | -7.597254 | -7.501667 | -7.598691 | -7.558832 |
| USDCHF | fGARCH.NGARCH | 3.745718e+00 | 2236 | 2.274000e-04 | 6494.4198134 | -19.819185 | -19.723598 | -19.820622 | -19.780763 |
| USDCHF | fGARCH.NAGARCH | 2.155107e+287 | 2236 | -1.927645e+284 | 358.5205739 | -6.527131 | -6.431544 | -6.528568 | -6.488708 |
| USDCHF | fGARCH.GJRGARCH | 5.430000e-05 | 2236 | 3.577800e-03 | 0.4260898 | -7.635906 | -7.540319 | -7.637343 | -7.597483 |
| USDCHF | gjrGARCH | 5.410000e-05 | 2236 | 3.577800e-03 | 0.4277262 | -7.658412 | -7.562825 | -7.659849 | -7.619989 |
| USDCHF | iGARCH | 2.713000e-04 | 2236 | 3.577600e-03 | 0.5951953 | -7.524153 | -7.455878 | -7.524918 | -7.496709 |
| USDCHF | csGARCH | 1.391000e-04 | 2236 | 3.577700e-03 | 0.5033270 | -7.557460 | -7.448218 | -7.559313 | -7.513548 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 4.000000e-07 | 2236 | 3.577800e-03 | 0.1874770 | -8.057212 | -7.975944 | -8.058271 | -8.024546 |
| USDCAD | fGARCH.GARCH | 4.000000e-07 | 2236 | 3.577800e-03 | 0.1875521 | -8.057192 | -7.975923 | -8.058251 | -8.024525 |
| USDCAD | fGARCH.TGARCH | 1.200000e-06 | 2236 | 3.577800e-03 | 0.6410392 | -7.831225 | -7.736303 | -7.832644 | -7.793070 |
| USDCAD | fGARCH.NGARCH | 7.664560e+119 | 2236 | -6.855600e+116 | 8875.3509577 | -25.027413 | -24.932491 | -25.028831 | -24.989258 |
| USDCAD | fGARCH.NAGARCH | 3.000000e-07 | 2236 | 3.577800e-03 | 0.1870218 | -8.065685 | -7.970763 | -8.067104 | -8.027530 |
| USDCAD | fGARCH.GJRGARCH | 3.000000e-07 | 2236 | 3.577800e-03 | 0.1876002 | -8.060906 | -7.965984 | -8.062325 | -8.022751 |
| USDCAD | gjrGARCH | 3.000000e-07 | 2236 | 3.577800e-03 | 0.1860144 | -8.066548 | -7.971626 | -8.067967 | -8.028393 |
| USDCAD | iGARCH | 5.000000e-07 | 2236 | 3.577800e-03 | 0.1891828 | -8.056657 | -7.989041 | -8.057409 | -8.029478 |
| USDCAD | csGARCH | 4.000000e-07 | 2236 | 3.577800e-03 | 0.1854206 | -8.041441 | -7.932866 | -8.043273 | -7.997798 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 5.853000e-04 | 2236 | 3.577300e-03 | 1.2136315 | -6.543910 | -6.454648 | -6.545171 | -6.508031 |
| USDCNY | fGARCH.GARCH | 3.669000e-04 | 2236 | 3.577500e-03 | 1.2155462 | -6.543360 | -6.454098 | -6.544621 | -6.507481 |
| USDCNY | fGARCH.TGARCH | 1.341655e+04 | 2236 | -1.199692e+01 | 4.0387293 | -6.265960 | -6.163056 | -6.267612 | -6.224598 |
| USDCNY | fGARCH.NGARCH | 2.171450e+02 | 2236 | -1.906485e-01 | 6629.7392604 | -18.299677 | -18.196773 | -18.301329 | -18.258315 |
| USDCNY | fGARCH.NAGARCH | 3.265008e+02 | 2236 | -2.884623e-01 | 26.8084491 | -6.353122 | -6.250217 | -6.354774 | -6.311759 |
| USDCNY | fGARCH.GJRGARCH | 1.944250e-02 | 2236 | 3.560400e-03 | 6.2854180 | -6.497338 | -6.394434 | -6.498990 | -6.455976 |
| USDCNY | gjrGARCH | 5.185000e-04 | 2236 | 3.577400e-03 | 1.2006618 | -6.583577 | -6.480672 | -6.585229 | -6.542214 |
| USDCNY | iGARCH | 7.443000e-04 | 2236 | 3.577200e-03 | 1.3212583 | -6.506358 | -6.430739 | -6.507282 | -6.475962 |
| USDCNY | csGARCH | 6.272000e-04 | 2236 | 3.577300e-03 | 1.3686447 | -6.531051 | -6.414504 | -6.533146 | -6.484205 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 1.121510e-02 | 2236 | 3.567800e-03 | 0.1881739 | 1.589979 | 1.678876 | 1.588700 | 1.625711 |
| USDJPY | fGARCH.GARCH | 1.113200e-02 | 2236 | 3.567900e-03 | 0.1879695 | 1.590212 | 1.679109 | 1.588933 | 1.625944 |
| USDJPY | fGARCH.TGARCH | 1.216363e+176 | 2236 | -1.087982e+173 | 83.7014653 | 1.799893 | 1.902432 | 1.798225 | 1.841109 |
| USDJPY | fGARCH.NGARCH | 7.432149e+245 | 2236 | -6.647719e+242 | 7505.0327538 | -12.113819 | -12.011279 | -12.115487 | -12.072603 |
| USDJPY | fGARCH.NAGARCH | 7.675100e-03 | 2236 | 3.571000e-03 | 0.1976159 | 1.574545 | 1.677085 | 1.572877 | 1.615761 |
| USDJPY | fGARCH.GJRGARCH | 9.290300e-03 | 2236 | 3.569500e-03 | 0.1930752 | 1.585747 | 1.688286 | 1.584078 | 1.626962 |
| USDJPY | gjrGARCH | 8.264100e-03 | 2236 | 3.570400e-03 | 0.1998324 | 1.576720 | 1.679259 | 1.575052 | 1.617936 |
| USDJPY | iGARCH | 1.114260e-02 | 2236 | 3.567900e-03 | 0.1899926 | 1.587496 | 1.662750 | 1.586552 | 1.617744 |
| USDJPY | csGARCH | 1.373920e-02 | 2236 | 3.565500e-03 | 0.1841325 | 1.597237 | 1.713419 | 1.595128 | 1.643936 |
6.1.2.2A : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 1.694000e-03 | 15652 | 5.109000e-04 | 11.78981 | -6.486888 | -6.403177 | -6.488014 | -6.453240 |
| fGARCH.GARCH | 1.651000e-03 | 15652 | 5.109000e-04 | 11.79008 | -6.486636 | -6.402924 | -6.487761 | -6.452987 |
| fGARCH.TGARCH | 1.737662e+175 | 15652 | -2.220371e+171 | 33.25741 | -6.265567 | -6.168208 | -6.267062 | -6.226433 |
| fGARCH.NGARCH | 1.061736e+245 | 15652 | -1.356677e+241 | 7190.60381 | -19.340474 | -19.243114 | -19.341969 | -19.301339 |
| fGARCH.NAGARCH | 3.078724e+286 | 15652 | -3.933969e+282 | 83.38656 | -6.224020 | -6.126660 | -6.225515 | -6.184886 |
| fGARCH.GJRGARCH | 4.112700e-03 | 15652 | 5.106000e-04 | 12.52896 | -6.489775 | -6.392415 | -6.491270 | -6.450641 |
| gjrGARCH | 1.262600e-03 | 15652 | 5.110000e-04 | 11.81364 | -6.512557 | -6.415197 | -6.514052 | -6.473423 |
| iGARCH | 3.411703e+286 | 15652 | -4.359446e+282 | 47.26923 | -6.423541 | -6.353479 | -6.424352 | -6.395379 |
| csGARCH | 2.072500e-03 | 15652 | 5.109000e-04 | 11.78669 | -6.469049 | -6.358040 | -6.470966 | -6.424428 |
6.1.2.2B : Table summary
| .id | Model | Date | Type | Price | Price.T1 | Akaike | Bayes | Shibata | Hannan.Quinn | diff | se |
|---|---|---|---|---|---|---|---|---|---|---|---|
| USDAUD | fGARCH.TGARCH | 2013-06-03 | USDAUD.Op | 1.02600 | -7.365624e+01 | 24.941247 | 25.064162 | 24.938973 | 24.990655 | 7.178971e+01 | 1 |
| USDAUD | fGARCH.NGARCH | 2013-06-27 | USDAUD.Lo | 1.07700 | 2.542027e+00 | -590.320340 | -590.197426 | -590.322615 | -590.270933 | 2.360285e+00 | 1 |
| USDAUD | fGARCH.NGARCH | 2014-04-14 | USDAUD.Op | 1.06200 | 1.419924e+09 | -416.149142 | -416.012570 | -416.151936 | -416.094244 | 1.337028e+09 | 1 |
| USDAUD | fGARCH.NGARCH | 2014-07-24 | USDAUD.Hi | 1.06400 | 2.487249e+34 | -502.592743 | -502.428857 | -502.596729 | -502.526867 | 2.337640e+34 | 1 |
| USDAUD | fGARCH.NAGARCH | 2015-02-09 | USDAUD.Op | 1.28800 | 9.042209e+09 | 101.921621 | 102.058192 | 101.918826 | 101.976518 | 7.020349e+09 | 1 |
| USDAUD | fGARCH.NAGARCH | 2015-02-10 | USDAUD.Op | 1.28300 | -9.623617e+31 | 153.814604 | 153.950801 | 153.811831 | 153.869344 | 7.500870e+31 | 1 |
| USDAUD | iGARCH | 2014-10-15 | USDAUD.Cl | 1.13730 | 2.310843e+145 | 738.699064 | 738.808021 | 738.697272 | 738.742856 | 2.031868e+145 | 1 |
| USDEUR | fGARCH.NGARCH | 2015-03-02 | USDEUR.Lo | 0.89000 | -4.015994e+07 | 83.346290 | 83.510176 | 83.342305 | 83.412167 | 4.512353e+07 | 1 |
| USDEUR | fGARCH.NGARCH | 2015-06-04 | USDEUR.Lo | 0.88700 | -1.394863e+18 | -545.380537 | -545.244340 | -545.383310 | -545.325796 | 1.572562e+18 | 1 |
| USDEUR | fGARCH.NGARCH | 2015-06-24 | USDEUR.Lo | 0.89100 | 1.892803e+10 | 77.586765 | 77.722962 | 77.583992 | 77.641506 | 2.124358e+10 | 1 |
| USDGBP | fGARCH.TGARCH | 2014-06-19 | USDGBP.Lo | 0.58600 | -3.465523e+73 | 364.832355 | 365.037213 | 364.826216 | 364.914701 | 5.913861e+73 | 1 |
| USDGBP | fGARCH.NGARCH | 2014-03-31 | USDGBP.Cl | 0.60001 | -1.642110e+04 | -444.661563 | -444.524991 | -444.664357 | -444.606666 | 2.736805e+04 | 1 |
| USDGBP | fGARCH.NGARCH | 2014-06-19 | USDGBP.Lo | 0.58600 | 4.316118e-01 | -160.018385 | -159.813528 | -160.024525 | -159.936039 | 7.365389e-01 | 1 |
| USDGBP | fGARCH.NGARCH | 2015-04-16 | USDGBP.Cl | 0.67016 | 1.865748e+15 | -556.647438 | -556.511242 | -556.650211 | -556.592698 | 2.784033e+15 | 1 |
| USDGBP | fGARCH.NGARCH | 2015-04-21 | USDGBP.Op | 0.67000 | -1.002521e+06 | -574.983967 | -574.847770 | -574.986740 | -574.929227 | 1.496300e+06 | 1 |
| USDGBP | fGARCH.NGARCH | 2015-06-08 | USDGBP.Op | 0.65200 | 5.022905e+36 | -490.210255 | -490.087678 | -490.212512 | -490.160989 | 7.703841e+36 | 1 |
| USDCHF | sGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.189676e+00 | -6.687989 | -6.606271 | -6.689007 | -6.655145 | 1.399619e+00 | 1 |
| USDCHF | fGARCH.GARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.189676e+00 | -6.687989 | -6.606271 | -6.689007 | -6.655145 | 1.399619e+00 | 1 |
| USDCHF | fGARCH.TGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.182560e+00 | -6.882116 | -6.786779 | -6.883495 | -6.843798 | 1.391247e+00 | 1 |
| USDCHF | fGARCH.NGARCH | 2013-12-12 | USDCHF.Op | 0.88700 | -3.879205e+00 | -432.539483 | -432.402912 | -432.542277 | -432.484586 | 4.373400e+00 | 1 |
| USDCHF | fGARCH.NGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.182556e+00 | -6.811955 | -6.716617 | -6.813334 | -6.773637 | 1.391243e+00 | 1 |
| USDCHF | fGARCH.NGARCH | 2015-09-07 | USDCHF.Lo | 0.97000 | -8.823318e+01 | -587.029347 | -586.920390 | -587.031140 | -586.985555 | 9.096204e+01 | 1 |
| USDCHF | fGARCH.NGARCH | 2015-10-30 | USDCHF.Hi | 0.99100 | -1.889325e+01 | -584.267632 | -584.158374 | -584.269437 | -584.223714 | 1.906483e+01 | 1 |
| USDCHF | fGARCH.NAGARCH | 2013-12-16 | USDCHF.Op | 0.89000 | 2.195181e+145 | 732.215372 | 732.352321 | 732.212557 | 732.270427 | 2.466495e+145 | 1 |
| USDCHF | fGARCH.NAGARCH | 2015-01-09 | USDCHF.Op | 1.01800 | -1.228938e+24 | 226.375920 | 226.539355 | 226.371964 | 226.441608 | 1.207208e+24 | 1 |
| USDCHF | fGARCH.NAGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.188451e+00 | -6.758750 | -6.663413 | -6.760129 | -6.720432 | 1.398178e+00 | 1 |
| USDCHF | fGARCH.GJRGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.189203e+00 | -6.775060 | -6.679723 | -6.776439 | -6.736742 | 1.399062e+00 | 1 |
| USDCHF | gjrGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.187461e+00 | -6.834457 | -6.739119 | -6.835835 | -6.796138 | 1.397013e+00 | 1 |
| USDCHF | iGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.189656e+00 | -6.696311 | -6.628212 | -6.697021 | -6.668940 | 1.399595e+00 | 1 |
| USDCHF | iGARCH | 2015-01-20 | USDCHF.Lo | 0.86900 | 1.169574e+00 | -6.632037 | -6.563939 | -6.632748 | -6.604667 | 1.345885e+00 | 1 |
| USDCHF | iGARCH | 2015-01-21 | USDCHF.Lo | 0.85100 | 5.536845e-01 | -6.599117 | -6.531019 | -6.599827 | -6.571747 | 6.506281e-01 | 1 |
| USDCHF | iGARCH | 2015-01-22 | USDCHF.Lo | 0.85300 | 1.132264e+00 | -6.569994 | -6.501896 | -6.570705 | -6.542624 | 1.327390e+00 | 1 |
| USDCHF | iGARCH | 2015-01-27 | USDCHF.Lo | 0.89400 | 6.896106e-01 | -6.470927 | -6.402829 | -6.471637 | -6.443557 | 7.713765e-01 | 1 |
| USDCHF | iGARCH | 2015-02-02 | USDCHF.Lo | 0.92000 | 7.319616e-01 | -6.350835 | -6.255235 | -6.352225 | -6.312407 | 7.956105e-01 | 1 |
| USDCHF | csGARCH | 2015-01-16 | USDCHF.Lo | 0.85000 | 1.193636e+00 | -6.688153 | -6.579196 | -6.689945 | -6.644361 | 1.404278e+00 | 1 |
| USDCHF | csGARCH | 2015-01-22 | USDCHF.Lo | 0.85300 | 1.141360e+00 | -6.534724 | -6.425767 | -6.536516 | -6.490932 | 1.338054e+00 | 1 |
| USDCHF | csGARCH | 2015-01-23 | USDCHF.Lo | 0.86800 | 6.200740e-01 | -6.493151 | -6.384194 | -6.494943 | -6.449359 | 7.143710e-01 | 1 |
| USDCAD | fGARCH.NGARCH | 2015-02-09 | USDCAD.Cl | 1.25170 | -7.979335e+22 | 142.673774 | 142.783031 | 142.671968 | 142.717692 | 6.374798e+22 | 1 |
| USDCAD | fGARCH.NGARCH | 2015-03-29 | USDCAD.Hi | 1.27000 | -6.542943e+22 | -529.240306 | -529.131049 | -529.242112 | -529.196389 | 5.151924e+22 | 1 |
| USDCAD | fGARCH.NGARCH | 2015-07-21 | USDCAD.Hi | 1.30500 | 4.139802e+61 | -435.142670 | -435.006474 | -435.145443 | -435.087930 | 3.172262e+61 | 1 |
| USDCNY | fGARCH.TGARCH | 2013-10-09 | USDCNY.Op | 6.11100 | 5.483283e+03 | 60.013013 | 60.135928 | 60.010739 | 60.062421 | 8.972808e+02 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-17 | USDCNY.Lo | 6.19200 | -3.142299e+01 | -584.776350 | -584.694407 | -584.777376 | -584.743412 | 5.074772e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-20 | USDCNY.Lo | 6.19500 | 1.601180e+01 | -588.464869 | -588.382700 | -588.465903 | -588.431836 | 2.584633e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-21 | USDCNY.Lo | 6.19300 | 1.802707e+02 | -584.204328 | -584.122385 | -584.205354 | -584.171390 | 2.910878e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-22 | USDCNY.Lo | 6.18900 | 6.023818e+01 | -586.383515 | -586.301572 | -586.384541 | -586.350577 | 9.733103e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-23 | USDCNY.Lo | 6.18200 | 1.116223e+02 | -582.294731 | -582.212788 | -582.295756 | -582.261792 | 1.805601e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-27 | USDCNY.Lo | 6.17600 | 4.872521e+01 | -587.187420 | -587.105250 | -587.188453 | -587.154387 | 7.889444e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-07-31 | USDCNY.Lo | 6.16300 | -1.151893e+02 | -587.546128 | -587.464185 | -587.547153 | -587.513189 | 1.869046e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-03 | USDCNY.Lo | 6.16800 | -1.481046e+00 | -591.735377 | -591.653208 | -591.736411 | -591.702344 | 2.401177e-01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-04 | USDCNY.Lo | 6.16100 | 1.118689e+01 | -590.853714 | -590.771771 | -590.854740 | -590.820775 | 1.815759e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-05 | USDCNY.Lo | 6.15300 | -5.459669e+01 | -563.148807 | -563.066864 | -563.149833 | -563.115869 | 8.873182e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-06 | USDCNY.Lo | 6.14700 | 2.635122e+01 | -591.728569 | -591.646626 | -591.729595 | -591.695631 | 4.286842e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-13 | USDCNY.Lo | 6.14200 | 4.004231e+02 | -583.022533 | -582.940590 | -583.023559 | -582.989595 | 6.519425e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-14 | USDCNY.Lo | 6.13600 | 4.872331e+01 | -586.351874 | -586.269931 | -586.352899 | -586.318935 | 7.940565e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-19 | USDCNY.Lo | 6.13000 | 3.981759e+01 | -587.532975 | -587.451032 | -587.534000 | -587.500036 | 6.495529e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-20 | USDCNY.Lo | 6.13000 | 1.169769e+02 | -586.017467 | -585.935524 | -586.018492 | -585.984528 | 1.908270e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-21 | USDCNY.Lo | 6.14100 | 5.744849e+01 | -586.508501 | -586.426558 | -586.509527 | -586.475563 | 9.354907e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-24 | USDCNY.Lo | 6.14000 | -3.247607e+01 | -589.174302 | -589.092132 | -589.175335 | -589.141269 | 5.289262e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-26 | USDCNY.Lo | 6.13300 | 9.738678e+01 | -587.251542 | -587.169599 | -587.252568 | -587.218604 | 1.587914e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-08-31 | USDCNY.Lo | 6.12900 | 2.545583e+02 | -584.923023 | -584.840853 | -584.924056 | -584.889989 | 4.153341e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-02 | USDCNY.Lo | 6.13100 | 1.578343e+00 | -590.429012 | -590.347069 | -590.430038 | -590.396074 | 2.574364e-01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-03 | USDCNY.Lo | 6.12500 | 3.759315e+01 | -581.281528 | -581.199585 | -581.282554 | -581.248590 | 6.137657e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-04 | USDCNY.Lo | 6.12800 | -4.565334e+01 | -589.259505 | -589.177562 | -589.260531 | -589.226567 | 7.449958e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-07 | USDCNY.Lo | 6.13000 | 7.649639e+01 | -580.676871 | -580.594702 | -580.677904 | -580.643838 | 1.247902e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-08 | USDCNY.Lo | 6.12200 | -2.517129e+01 | -587.872377 | -587.790434 | -587.873402 | -587.839438 | 4.111612e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-11 | USDCNY.Lo | 6.12000 | -3.251440e+01 | -587.456738 | -587.374795 | -587.457764 | -587.423800 | 5.312810e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-14 | USDCNY.Lo | 6.12500 | -1.796358e+02 | -584.617601 | -584.535431 | -584.618634 | -584.584568 | 2.932830e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-15 | USDCNY.Lo | 6.13200 | -1.112814e+01 | -590.468673 | -590.386730 | -590.469698 | -590.435734 | 1.814765e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-16 | USDCNY.Lo | 6.12900 | -1.759094e+02 | -585.597533 | -585.515590 | -585.598558 | -585.564594 | 2.870116e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-09-30 | USDCNY.Lo | 6.12800 | 1.553160e+02 | -567.572804 | -567.490861 | -567.573830 | -567.539866 | 2.534531e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-10-01 | USDCNY.Lo | 6.12800 | -1.146657e+02 | -584.091459 | -584.009516 | -584.092485 | -584.058521 | 1.871177e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-10-06 | USDCNY.Lo | 6.12900 | 2.295707e+02 | -583.286508 | -583.204565 | -583.287534 | -583.253570 | 3.745647e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-10-07 | USDCNY.Lo | 6.12500 | 5.146397e+01 | -565.845084 | -565.763141 | -565.846110 | -565.812146 | 8.402281e+00 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-10-09 | USDCNY.Lo | 6.12000 | 6.182692e+01 | -583.758544 | -583.676826 | -583.759562 | -583.725700 | 1.010244e+01 | 1 |
| USDCNY | fGARCH.NGARCH | 2014-11-26 | USDCNY.Lo | 6.12300 | 6.187566e+01 | -583.601907 | -583.520189 | -583.602924 | -583.569062 | 1.010545e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-07-24 | USDCNY.Lo | 6.18200 | -3.603032e+02 | 14.561667 | 14.643610 | 14.560642 | 14.594606 | 5.828262e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-07-31 | USDCNY.Lo | 6.16300 | -3.531901e+02 | 14.522470 | 14.604413 | 14.521444 | 14.555409 | 5.730814e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-08-04 | USDCNY.Lo | 6.16100 | -3.492923e+02 | 14.548440 | 14.630382 | 14.547414 | 14.581378 | 5.669409e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-08-26 | USDCNY.Lo | 6.13300 | 4.865151e+00 | 104.667516 | 104.749459 | 104.666490 | 104.700454 | 7.932742e-01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-09-04 | USDCNY.Lo | 6.12800 | 4.796821e+02 | 172.167572 | 172.249515 | 172.166546 | 172.200510 | 7.827710e+01 | 1 |
| USDCNY | fGARCH.NAGARCH | 2014-10-19 | USDCNY.Lo | 6.11300 | -3.344848e+02 | 98.972743 | 99.054686 | 98.971717 | 99.005682 | 5.471696e+01 | 1 |
| USDCNY | fGARCH.GJRGARCH | 2014-09-01 | USDCNY.Lo | 6.13200 | 1.263740e+01 | 98.054293 | 98.136236 | 98.053267 | 98.087231 | 2.060893e+00 | 1 |
| USDJPY | fGARCH.TGARCH | 2013-03-31 | USDJPY.Op | 94.26200 | -5.215159e+89 | 433.750440 | 433.914326 | 433.746455 | 433.816317 | 5.532621e+87 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-05-20 | USDJPY.Hi | 102.87200 | 1.639729e+20 | 126.895461 | 127.031657 | 126.892687 | 126.950201 | 1.593951e+18 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-06-16 | USDJPY.Hi | 95.10600 | -2.728130e+05 | 179.131969 | 179.268541 | 179.129175 | 179.186867 | 2.868516e+03 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-06-19 | USDJPY.Hi | 98.23900 | 4.076553e+124 | 740.361014 | 740.497210 | 740.358240 | 740.415754 | 4.149628e+122 | 1 |
| USDJPY | fGARCH.NGARCH | 2013-07-22 | USDJPY.Hi | 100.17000 | -7.099425e+16 | 107.520826 | 107.657022 | 107.518052 | 107.575566 | 7.087376e+14 | 1 |
6.1.2.2C : Table summary
Lastly, we filter all bias data and look at the comparison of mse of OHLC of 7 currencies.
## filter all date which excludes bias and also contain OHLC of 7 currencies.
united.fx3 <- united.fx2 %>% dplyr::filter(!Date %in% ntimeID)
acc <- united.fx3 %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
6.1.2.3A : Table summary
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 0.0000006 | 1952 | 0.0040984 | 0.1708132 | -7.346575 | -7.267282 | -7.347576 | -7.314703 |
| USDAUD | fGARCH.GARCH | 0.0000006 | 1952 | 0.0040984 | 0.1707342 | -7.346631 | -7.267338 | -7.347632 | -7.314758 |
| USDAUD | fGARCH.TGARCH | 0.0000032 | 1952 | 0.0040984 | 0.6440620 | -7.103694 | -7.010748 | -7.105048 | -7.066333 |
| USDAUD | fGARCH.NGARCH | 0.0000060 | 1952 | 0.0040984 | 8450.4041131 | -23.049638 | -22.956692 | -23.050991 | -23.012277 |
| USDAUD | fGARCH.NAGARCH | 0.0000006 | 1952 | 0.0040984 | 30.6436172 | -7.229818 | -7.136872 | -7.231172 | -7.192457 |
| USDAUD | fGARCH.GJRGARCH | 0.0000008 | 1952 | 0.0040984 | 0.1783820 | -7.347261 | -7.254315 | -7.348614 | -7.309900 |
| USDAUD | gjrGARCH | 0.0000008 | 1952 | 0.0040984 | 0.1806183 | -7.354037 | -7.261091 | -7.355390 | -7.316676 |
| USDAUD | iGARCH | 0.0000009 | 1952 | 0.0040984 | 0.1747670 | -7.349048 | -7.283409 | -7.349751 | -7.322664 |
| USDAUD | csGARCH | 0.0000008 | 1952 | 0.0040984 | 0.1769349 | -7.328975 | -7.222375 | -7.330733 | -7.286125 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 0.0000004 | 1952 | 0.0040984 | 0.2991369 | -8.309326 | -8.226972 | -8.310406 | -8.276223 |
| USDEUR | fGARCH.GARCH | 0.0000004 | 1952 | 0.0040984 | 0.2989333 | -8.309453 | -8.227099 | -8.310533 | -8.276350 |
| USDEUR | fGARCH.TGARCH | 0.0000010 | 1952 | 0.0040984 | 0.4973797 | -8.158503 | -8.062496 | -8.159947 | -8.119912 |
| USDEUR | fGARCH.NGARCH | 0.0000029 | 1952 | 0.0040984 | 8890.5130604 | -22.924074 | -22.828066 | -22.925518 | -22.885482 |
| USDEUR | fGARCH.NAGARCH | 0.0000004 | 1952 | 0.0040984 | 35.0564421 | -8.184321 | -8.088314 | -8.185766 | -8.145730 |
| USDEUR | fGARCH.GJRGARCH | 0.0000004 | 1952 | 0.0040984 | 0.3023249 | -8.317832 | -8.221825 | -8.319277 | -8.279241 |
| USDEUR | gjrGARCH | 0.0000004 | 1952 | 0.0040984 | 0.3047685 | -8.335397 | -8.239390 | -8.336842 | -8.296806 |
| USDEUR | iGARCH | 0.0000004 | 1952 | 0.0040984 | 0.2984837 | -8.308504 | -8.239804 | -8.309274 | -8.280889 |
| USDEUR | csGARCH | 0.0000005 | 1952 | 0.0040984 | 0.2855177 | -8.296165 | -8.186505 | -8.298027 | -8.252086 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 0.0000001 | 1952 | 0.0040984 | 0.1045807 | -9.012202 | -8.931556 | -9.013258 | -8.979787 |
| USDGBP | fGARCH.GARCH | 0.0000001 | 1952 | 0.0040984 | 0.1043417 | -9.012343 | -8.931697 | -9.013399 | -8.979928 |
| USDGBP | fGARCH.TGARCH | 0.0000002 | 1952 | 0.0040984 | 0.4526637 | -8.743122 | -8.648838 | -8.744535 | -8.705225 |
| USDGBP | fGARCH.NGARCH | 0.0000004 | 1952 | 0.0040984 | 3314.7033419 | -13.991083 | -13.896799 | -13.992496 | -13.953186 |
| USDGBP | fGARCH.NAGARCH | 0.0000001 | 1952 | 0.0040984 | 22.5228861 | -8.830478 | -8.736194 | -8.831891 | -8.792582 |
| USDGBP | fGARCH.GJRGARCH | 0.0000001 | 1952 | 0.0040984 | 0.1084197 | -9.025494 | -8.931209 | -9.026907 | -8.987597 |
| USDGBP | gjrGARCH | 0.0000001 | 1952 | 0.0040984 | 0.1057182 | -9.038819 | -8.944535 | -9.040232 | -9.000922 |
| USDGBP | iGARCH | 0.0000001 | 1952 | 0.0040984 | 0.1048222 | -9.012737 | -8.945730 | -9.013490 | -8.985804 |
| USDGBP | csGARCH | 0.0000001 | 1952 | 0.0040984 | 0.0909887 | -8.998238 | -8.890315 | -9.000061 | -8.954859 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 0.0000050 | 1952 | 0.0040984 | 0.4334753 | -7.550708 | -7.468881 | -7.551776 | -7.517816 |
| USDCHF | fGARCH.GARCH | 0.0000050 | 1952 | 0.0040984 | 0.4340160 | -7.550196 | -7.468368 | -7.551264 | -7.517304 |
| USDCHF | fGARCH.TGARCH | 0.0000029 | 1952 | 0.0040984 | 0.5851206 | -7.545230 | -7.449746 | -7.546660 | -7.506849 |
| USDCHF | fGARCH.NGARCH | 0.0000040 | 1952 | 0.0040984 | 6474.5668887 | -19.502392 | -19.406909 | -19.503823 | -19.464011 |
| USDCHF | fGARCH.NAGARCH | 0.0000026 | 1952 | 0.0040984 | 76.2343749 | -6.937068 | -6.841585 | -6.938499 | -6.898687 |
| USDCHF | fGARCH.GJRGARCH | 0.0000030 | 1952 | 0.0040984 | 0.4008434 | -7.588103 | -7.492619 | -7.589533 | -7.549722 |
| USDCHF | gjrGARCH | 0.0000034 | 1952 | 0.0040984 | 0.4087041 | -7.608373 | -7.512890 | -7.609803 | -7.569992 |
| USDCHF | iGARCH | 0.0000801 | 1952 | 0.0040983 | 0.5668713 | -7.473306 | -7.405135 | -7.474066 | -7.445904 |
| USDCHF | csGARCH | 0.0000245 | 1952 | 0.0040983 | 0.4682931 | -7.512004 | -7.402865 | -7.513850 | -7.468134 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 0.0000004 | 1952 | 0.0040984 | 0.1950430 | -8.033957 | -7.953125 | -8.035003 | -8.001466 |
| USDCAD | fGARCH.GARCH | 0.0000004 | 1952 | 0.0040984 | 0.1951551 | -8.034016 | -7.953184 | -8.035061 | -8.001524 |
| USDCAD | fGARCH.TGARCH | 0.0000013 | 1952 | 0.0040984 | 0.6818771 | -7.795452 | -7.700967 | -7.796856 | -7.757473 |
| USDCAD | fGARCH.NGARCH | 0.0000090 | 1952 | 0.0040984 | 9311.7531360 | -26.002813 | -25.908328 | -26.004217 | -25.964834 |
| USDCAD | fGARCH.NAGARCH | 0.0000003 | 1952 | 0.0040984 | 0.1944680 | -8.041987 | -7.947502 | -8.043391 | -8.004008 |
| USDCAD | fGARCH.GJRGARCH | 0.0000003 | 1952 | 0.0040984 | 0.1955054 | -8.037987 | -7.943503 | -8.039391 | -8.000008 |
| USDCAD | gjrGARCH | 0.0000003 | 1952 | 0.0040984 | 0.1936610 | -8.043600 | -7.949116 | -8.045004 | -8.005621 |
| USDCAD | iGARCH | 0.0000004 | 1952 | 0.0040984 | 0.1972246 | -8.033364 | -7.966185 | -8.034105 | -8.006360 |
| USDCAD | csGARCH | 0.0000004 | 1952 | 0.0040984 | 0.1929526 | -8.018045 | -7.909907 | -8.019861 | -7.974578 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 0.0005777 | 1952 | 0.0040978 | 0.9559600 | -6.599860 | -6.509652 | -6.601148 | -6.563601 |
| USDCNY | fGARCH.GARCH | 0.0003334 | 1952 | 0.0040980 | 0.9588634 | -6.599179 | -6.508972 | -6.600467 | -6.562920 |
| USDCNY | fGARCH.TGARCH | 0.0010342 | 1952 | 0.0040973 | 2.0011508 | -6.341245 | -6.237396 | -6.342927 | -6.299503 |
| USDCNY | fGARCH.NGARCH | 0.0011275 | 1952 | 0.0040972 | 1577.7891946 | -9.329087 | -9.225239 | -9.330770 | -9.287346 |
| USDCNY | fGARCH.NAGARCH | 0.0002131 | 1952 | 0.0040981 | 1.2029455 | -6.608325 | -6.504476 | -6.610007 | -6.566583 |
| USDCNY | fGARCH.GJRGARCH | 0.0004724 | 1952 | 0.0040979 | 1.1224156 | -6.600681 | -6.496832 | -6.602363 | -6.558939 |
| USDCNY | gjrGARCH | 0.0004996 | 1952 | 0.0040978 | 0.9596450 | -6.639823 | -6.535974 | -6.641505 | -6.598081 |
| USDCNY | iGARCH | 0.0006325 | 1952 | 0.0040977 | 1.0976028 | -6.557338 | -6.480772 | -6.558284 | -6.526562 |
| USDCNY | csGARCH | 0.0006490 | 1952 | 0.0040977 | 1.1240780 | -6.584270 | -6.466779 | -6.586398 | -6.537044 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 0.0120652 | 1952 | 0.0040860 | 0.1822168 | 1.632333 | 1.721165 | 1.631055 | 1.668039 |
| USDJPY | fGARCH.GARCH | 0.0118707 | 1952 | 0.0040862 | 0.1821128 | 1.632480 | 1.721311 | 1.631201 | 1.668185 |
| USDJPY | fGARCH.TGARCH | 0.0137785 | 1952 | 0.0040842 | 0.2175220 | 1.649415 | 1.751888 | 1.647748 | 1.690604 |
| USDJPY | fGARCH.NGARCH | 0.0717309 | 1952 | 0.0040249 | 7215.6958366 | -12.574166 | -12.471693 | -12.575833 | -12.532977 |
| USDJPY | fGARCH.NAGARCH | 0.0080002 | 1952 | 0.0040902 | 0.1920120 | 1.617307 | 1.719780 | 1.615640 | 1.658496 |
| USDJPY | fGARCH.GJRGARCH | 0.0097116 | 1952 | 0.0040884 | 0.1870475 | 1.628468 | 1.730941 | 1.626802 | 1.669657 |
| USDJPY | gjrGARCH | 0.0086886 | 1952 | 0.0040895 | 0.1936266 | 1.620182 | 1.722655 | 1.618515 | 1.661371 |
| USDJPY | iGARCH | 0.0119665 | 1952 | 0.0040861 | 0.1839926 | 1.630166 | 1.705356 | 1.629223 | 1.660389 |
| USDJPY | csGARCH | 0.0151578 | 1952 | 0.0040828 | 0.1780868 | 1.639479 | 1.755594 | 1.637372 | 1.686151 |
6.1.2.3B : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 0.0018071 | 13664 | 0.0005852 | 11.74763 | -6.460042 | -6.376615 | -6.461159 | -6.426508 |
| fGARCH.GARCH | 0.0017444 | 13664 | 0.0005852 | 11.74841 | -6.459905 | -6.376478 | -6.461022 | -6.426371 |
| fGARCH.TGARCH | 0.0021173 | 13664 | 0.0005852 | 11.73284 | -6.291119 | -6.194043 | -6.292604 | -6.252099 |
| fGARCH.NGARCH | 0.0104115 | 13664 | 0.0005840 | 6495.98565 | -18.196179 | -18.099104 | -18.197664 | -18.157159 |
| fGARCH.NAGARCH | 0.0011739 | 13664 | 0.0005853 | 34.72609 | -6.316384 | -6.219309 | -6.317869 | -6.277364 |
| fGARCH.GJRGARCH | 0.0014555 | 13664 | 0.0005853 | 11.78865 | -6.469841 | -6.372766 | -6.471326 | -6.430821 |
| gjrGARCH | 0.0013133 | 13664 | 0.0005853 | 11.77958 | -6.485695 | -6.388620 | -6.487180 | -6.446675 |
| iGARCH | 0.0018116 | 13664 | 0.0005852 | 11.75832 | -6.443447 | -6.373668 | -6.444249 | -6.415399 |
| csGARCH | 0.0022619 | 13664 | 0.0005851 | 11.74789 | -6.442602 | -6.331879 | -6.444508 | -6.398096 |
6.1.2.3C : Table summary
## filtered bias closing price.
op <- fx %>% separate(Type, c('Cur', 'Type')) %>%
dplyr::filter(Type == 'Op') %>%
dplyr::select(-Cur, -Type)
ntmID <- op %>% dplyr::filter(se == 1) %>% .$Date %>% unlist %>% sort
acc <- op %>% dplyr::filter(!Date %in% ntmID & Date %in% ntimeID2) %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 0.0000010 | 544 | 0.0147059 | 1.496250e-01 | -7.273581 | -7.192119 | -7.274640 | -7.240836 |
| USDAUD | fGARCH.GARCH | 0.0000011 | 544 | 0.0147059 | 1.493904e-01 | -7.273323 | -7.191861 | -7.274382 | -7.240578 |
| USDAUD | fGARCH.TGARCH | 0.0000027 | 544 | 0.0147059 | 4.388638e-01 | -7.098803 | -7.003688 | -7.100223 | -7.060570 |
| USDAUD | fGARCH.AVGARCH | 0.0000002 | 52 | 0.1538461 | 4.323170e-02 | -7.644820 | -7.531890 | -7.646799 | -7.599426 |
| USDAUD | fGARCH.NGARCH | 0.0000040 | 544 | 0.0147059 | 4.973318e+03 | -16.256002 | -16.160888 | -16.257423 | -16.217770 |
| USDAUD | fGARCH.NAGARCH | 0.0000009 | 544 | 0.0147059 | 1.564530e-01 | -7.284464 | -7.189349 | -7.285884 | -7.246232 |
| USDAUD | fGARCH.APARCH | 0.0000005 | 214 | 0.0373832 | 1.601340e+03 | -10.070397 | -9.962779 | -10.072204 | -10.027137 |
| USDAUD | fGARCH.GJRGARCH | 0.0000010 | 544 | 0.0147059 | 1.520530e-01 | -7.277768 | -7.182653 | -7.279188 | -7.239535 |
| USDAUD | fGARCH.ALLGARCH | 0.0000021 | 119 | 0.0672269 | 6.386576e+02 | -9.956839 | -9.826085 | -9.959472 | -9.904280 |
| USDAUD | eGARCH | 0.0000009 | 369 | 0.0216802 | 6.879100e-02 | -7.450577 | -7.356177 | -7.451987 | -7.412631 |
| USDAUD | gjrGARCH | 0.0000010 | 544 | 0.0147059 | 1.545679e-01 | -7.285608 | -7.190494 | -7.287029 | -7.247376 |
| USDAUD | apARCH | 0.0000004 | 81 | 0.0987654 | 3.347000e-03 | -7.724934 | -7.606725 | -7.727111 | -7.677418 |
| USDAUD | iGARCH | 0.0000011 | 544 | 0.0147059 | 1.487704e-01 | -7.278342 | -7.210534 | -7.279094 | -7.251086 |
| USDAUD | csGARCH | 0.0000013 | 544 | 0.0147059 | 1.525311e-01 | -7.256040 | -7.147272 | -7.257874 | -7.212319 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 0.0000004 | 544 | 0.0147059 | 3.296896e-01 | -8.259009 | -8.175690 | -8.260111 | -8.225518 |
| USDEUR | fGARCH.GARCH | 0.0000004 | 544 | 0.0147059 | 3.297296e-01 | -8.258956 | -8.175638 | -8.260059 | -8.225466 |
| USDEUR | fGARCH.TGARCH | 0.0000006 | 544 | 0.0147059 | 5.520876e-01 | -8.130113 | -8.033141 | -8.131583 | -8.091134 |
| USDEUR | fGARCH.AVGARCH | 0.0000000 | 26 | 0.3076923 | 8.860980e-02 | -7.884639 | -7.783841 | -7.886225 | -7.844123 |
| USDEUR | fGARCH.NGARCH | 0.0000010 | 544 | 0.0147059 | 4.762254e+03 | -15.387019 | -15.290047 | -15.388490 | -15.348040 |
| USDEUR | fGARCH.NAGARCH | 0.0000004 | 544 | 0.0147059 | 3.350123e-01 | -8.265527 | -8.168555 | -8.266998 | -8.226548 |
| USDEUR | fGARCH.APARCH | 0.0000000 | 93 | 0.0860215 | 2.065288e+01 | -7.325212 | -7.225203 | -7.326756 | -7.285012 |
| USDEUR | fGARCH.GJRGARCH | 0.0000003 | 544 | 0.0147059 | 3.374228e-01 | -8.269006 | -8.172035 | -8.270477 | -8.230028 |
| USDEUR | fGARCH.ALLGARCH | 0.0000001 | 226 | 0.0353982 | 1.528688e+03 | -10.819426 | -10.698045 | -10.821672 | -10.770633 |
| USDEUR | eGARCH | 0.0000003 | 371 | 0.0215633 | 4.140797e-01 | -8.468758 | -8.370562 | -8.470269 | -8.429286 |
| USDEUR | gjrGARCH | 0.0000003 | 544 | 0.0147059 | 3.422386e-01 | -8.283944 | -8.186972 | -8.285414 | -8.244965 |
| USDEUR | apARCH | 0.0000000 | 81 | 0.0987654 | 2.790000e-04 | -8.061228 | -7.961921 | -8.062750 | -8.021310 |
| USDEUR | iGARCH | 0.0000004 | 544 | 0.0147059 | 3.342271e-01 | -8.257891 | -8.188225 | -8.258679 | -8.229888 |
| USDEUR | csGARCH | 0.0000005 | 544 | 0.0147059 | 3.270210e-01 | -8.237897 | -8.127272 | -8.239788 | -8.193430 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 0.0000001 | 544 | 0.0147059 | 1.040953e-01 | -8.971158 | -8.886604 | -8.972326 | -8.937172 |
| USDGBP | fGARCH.GARCH | 0.0000001 | 544 | 0.0147059 | 1.040981e-01 | -8.971506 | -8.886952 | -8.972674 | -8.937520 |
| USDGBP | fGARCH.TGARCH | 0.0000002 | 544 | 0.0147059 | 5.529579e-01 | -8.662216 | -8.564022 | -8.663755 | -8.622747 |
| USDGBP | fGARCH.AVGARCH | 0.0000000 | 34 | 0.2352941 | 2.962751e+01 | -7.880450 | -7.784713 | -7.881841 | -7.841971 |
| USDGBP | fGARCH.NGARCH | 0.0000002 | 544 | 0.0147059 | 4.233400e+03 | -16.101632 | -16.003439 | -16.103172 | -16.062164 |
| USDGBP | fGARCH.NAGARCH | 0.0000001 | 544 | 0.0147059 | 2.737010e+01 | -8.758187 | -8.659993 | -8.759726 | -8.718718 |
| USDGBP | fGARCH.APARCH | 0.0000000 | 214 | 0.0373832 | 2.524498e-01 | -8.582954 | -8.479047 | -8.584644 | -8.541189 |
| USDGBP | fGARCH.GJRGARCH | 0.0000002 | 544 | 0.0147059 | 1.094037e-01 | -8.983553 | -8.885359 | -8.985092 | -8.944084 |
| USDGBP | fGARCH.ALLGARCH | 0.0000000 | 227 | 0.0352423 | 2.888485e-01 | -8.785055 | -8.665449 | -8.787275 | -8.736979 |
| USDGBP | eGARCH | 0.0000001 | 370 | 0.0216216 | 9.383410e+00 | -8.875106 | -8.775855 | -8.876691 | -8.835212 |
| USDGBP | gjrGARCH | 0.0000001 | 544 | 0.0147059 | 1.128006e-01 | -8.996872 | -8.898678 | -8.998411 | -8.957403 |
| USDGBP | apARCH | 0.0000000 | 81 | 0.0987654 | 1.845800e-03 | -9.076260 | -8.978906 | -9.077705 | -9.037131 |
| USDGBP | iGARCH | 0.0000001 | 544 | 0.0147059 | 1.038262e-01 | -8.971228 | -8.900313 | -8.972077 | -8.942724 |
| USDGBP | csGARCH | 0.0000001 | 544 | 0.0147059 | 1.026385e-01 | -8.950626 | -8.838793 | -8.952590 | -8.905675 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 0.0000039 | 544 | 0.0147059 | 4.929583e-01 | -7.477976 | -7.396162 | -7.479057 | -7.445090 |
| USDCHF | fGARCH.GARCH | 0.0000039 | 544 | 0.0147059 | 4.945251e-01 | -7.475772 | -7.393958 | -7.476853 | -7.442885 |
| USDCHF | fGARCH.TGARCH | 0.0000082 | 544 | 0.0147059 | 1.291473e+00 | -7.428334 | -7.332864 | -7.429777 | -7.389958 |
| USDCHF | fGARCH.AVGARCH | 0.0000002 | 16 | 0.5000000 | 2.541510e-02 | -7.687590 | -7.571104 | -7.689769 | -7.640760 |
| USDCHF | fGARCH.NGARCH | 0.0000027 | 544 | 0.0147059 | 6.913008e+03 | -23.548439 | -23.452970 | -23.549882 | -23.510064 |
| USDCHF | fGARCH.NAGARCH | 0.0000019 | 544 | 0.0147059 | 7.618680e+01 | -6.819252 | -6.723782 | -6.820695 | -6.780876 |
| USDCHF | fGARCH.APARCH | 0.0000002 | 213 | 0.0375587 | 1.055341e-01 | -7.504771 | -7.396081 | -7.506622 | -7.461078 |
| USDCHF | fGARCH.GJRGARCH | 0.0000024 | 544 | 0.0147059 | 4.629425e-01 | -7.521026 | -7.425556 | -7.522469 | -7.482650 |
| USDCHF | fGARCH.ALLGARCH | 0.0000014 | 225 | 0.0355555 | 8.962303e+03 | -22.631707 | -22.508883 | -22.634041 | -22.582333 |
| USDCHF | eGARCH | 0.0000003 | 370 | 0.0216216 | 1.051790e-01 | -7.936543 | -7.837500 | -7.938107 | -7.896730 |
| USDCHF | gjrGARCH | 0.0000024 | 544 | 0.0147059 | 4.587758e-01 | -7.547831 | -7.452361 | -7.549274 | -7.509455 |
| USDCHF | apARCH | 0.0000001 | 80 | 0.1000000 | 1.479400e-03 | -7.785639 | -7.682901 | -7.787292 | -7.744339 |
| USDCHF | iGARCH | 0.0000038 | 544 | 0.0147059 | 5.476870e-01 | -7.453627 | -7.385468 | -7.454399 | -7.426229 |
| USDCHF | csGARCH | 0.0000038 | 544 | 0.0147059 | 4.998638e-01 | -7.458442 | -7.349317 | -7.460301 | -7.414578 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 0.0000002 | 544 | 0.0147059 | 1.857258e-01 | -7.976085 | -7.896125 | -7.977111 | -7.943944 |
| USDCAD | fGARCH.GARCH | 0.0000002 | 544 | 0.0147059 | 1.855630e-01 | -7.976229 | -7.896269 | -7.977255 | -7.944088 |
| USDCAD | fGARCH.TGARCH | 0.0000008 | 544 | 0.0147059 | 4.684465e-01 | -7.774289 | -7.680675 | -7.775670 | -7.736660 |
| USDCAD | fGARCH.AVGARCH | 0.0000001 | 40 | 0.2000000 | 3.721640e-02 | -8.215637 | -8.105027 | -8.217508 | -8.171176 |
| USDCAD | fGARCH.NGARCH | 0.0000007 | 544 | 0.0147059 | 3.675945e+03 | -14.189054 | -14.095441 | -14.190435 | -14.151425 |
| USDCAD | fGARCH.NAGARCH | 0.0000002 | 544 | 0.0147059 | 1.851842e-01 | -7.983423 | -7.889810 | -7.984804 | -7.945794 |
| USDCAD | fGARCH.APARCH | 0.0000010 | 211 | 0.0379147 | 2.704998e+01 | -7.663218 | -7.557049 | -7.664968 | -7.620540 |
| USDCAD | fGARCH.GJRGARCH | 0.0000002 | 544 | 0.0147059 | 1.893419e-01 | -7.982959 | -7.889345 | -7.984340 | -7.945330 |
| USDCAD | fGARCH.ALLGARCH | 0.0000001 | 226 | 0.0353982 | 1.792432e+03 | -11.988171 | -11.867582 | -11.990406 | -11.939697 |
| USDCAD | eGARCH | 0.0000001 | 369 | 0.0216802 | 3.649920e-02 | -8.207173 | -8.114658 | -8.208515 | -8.169985 |
| USDCAD | gjrGARCH | 0.0000002 | 544 | 0.0147059 | 1.875037e-01 | -7.989684 | -7.896071 | -7.991065 | -7.952055 |
| USDCAD | apARCH | 0.0000001 | 80 | 0.1000000 | 2.793900e-03 | -8.290652 | -8.179173 | -8.292562 | -8.245841 |
| USDCAD | iGARCH | 0.0000002 | 544 | 0.0147059 | 1.885810e-01 | -7.974035 | -7.907728 | -7.974760 | -7.947382 |
| USDCAD | csGARCH | 0.0000002 | 544 | 0.0147059 | 1.823333e-01 | -7.960933 | -7.853667 | -7.962722 | -7.917816 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 0.0000059 | 544 | 0.0147059 | 2.005122e-01 | -6.865971 | -6.778289 | -6.867185 | -6.830727 |
| USDCNY | fGARCH.GARCH | 0.0000058 | 544 | 0.0147059 | 2.003218e-01 | -6.865070 | -6.777388 | -6.866283 | -6.829826 |
| USDCNY | fGARCH.TGARCH | 0.0000167 | 544 | 0.0147058 | 1.437315e+00 | -6.505910 | -6.404587 | -6.507509 | -6.465183 |
| USDCNY | fGARCH.AVGARCH | 0.0000005 | 12 | 0.6666666 | 3.583000e-04 | -6.991135 | -6.882277 | -6.992923 | -6.947384 |
| USDCNY | fGARCH.NGARCH | 0.0000088 | 544 | 0.0147059 | 3.135557e+03 | -12.291165 | -12.189841 | -12.292763 | -12.250438 |
| USDCNY | fGARCH.NAGARCH | 0.0000053 | 544 | 0.0147059 | 1.933519e-01 | -6.900901 | -6.799577 | -6.902500 | -6.860174 |
| USDCNY | fGARCH.APARCH | 0.0013318 | 211 | 0.0379021 | 3.456613e+04 | -72.067307 | -71.945959 | -72.069548 | -72.018531 |
| USDCNY | fGARCH.GJRGARCH | 0.0000062 | 544 | 0.0147059 | 1.895800e-01 | -6.897659 | -6.796335 | -6.899258 | -6.856932 |
| USDCNY | fGARCH.ALLGARCH | 0.0000490 | 226 | 0.0353978 | 3.002171e+03 | -11.855494 | -11.719672 | -11.858283 | -11.800901 |
| USDCNY | eGARCH | 0.0000129 | 367 | 0.0217983 | 2.384204e-01 | -6.831413 | -6.725326 | -6.833155 | -6.788771 |
| USDCNY | gjrGARCH | 0.0000066 | 544 | 0.0147059 | 1.793100e-01 | -6.912884 | -6.811560 | -6.914482 | -6.872156 |
| USDCNY | apARCH | 0.0000129 | 81 | 0.0987651 | 6.340900e-02 | -6.762205 | -6.645174 | -6.764310 | -6.715168 |
| USDCNY | iGARCH | 0.0000071 | 544 | 0.0147059 | 2.064925e-01 | -6.854494 | -6.780455 | -6.855376 | -6.824734 |
| USDCNY | csGARCH | 0.0000094 | 544 | 0.0147058 | 2.146035e-01 | -6.888253 | -6.773287 | -6.890288 | -6.842042 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 0.0099476 | 544 | 0.0146693 | 1.734215e-01 | 1.718843 | 1.806255 | 1.717603 | 1.753978 |
| USDJPY | fGARCH.GARCH | 0.0093742 | 544 | 0.0146714 | 1.734193e-01 | 1.718921 | 1.806334 | 1.717681 | 1.754056 |
| USDJPY | fGARCH.TGARCH | 0.0056426 | 544 | 0.0146851 | 1.825938e-01 | 1.723283 | 1.824339 | 1.721661 | 1.763902 |
| USDJPY | fGARCH.AVGARCH | 0.1450546 | 40 | 0.1927473 | 1.221420e+00 | 1.313452 | 1.451011 | 1.310536 | 1.368740 |
| USDJPY | fGARCH.NGARCH | 0.0120317 | 544 | 0.0146616 | 9.500955e+03 | -17.403297 | -17.302242 | -17.404920 | -17.362678 |
| USDJPY | fGARCH.NAGARCH | 0.0049086 | 544 | 0.0146878 | 1.843713e-01 | 1.706119 | 1.807174 | 1.704497 | 1.746738 |
| USDJPY | fGARCH.APARCH | 0.0224658 | 96 | 0.0828653 | 1.617204e+04 | -25.235513 | -25.109664 | -25.238025 | -25.184931 |
| USDJPY | fGARCH.GJRGARCH | 0.0071839 | 544 | 0.0146795 | 1.797261e-01 | 1.715066 | 1.816121 | 1.713443 | 1.755685 |
| USDJPY | fGARCH.ALLGARCH | 0.0299952 | 199 | 0.0398995 | 8.797060e+03 | -16.069967 | -15.946816 | -16.072338 | -16.020467 |
| USDJPY | eGARCH | 0.0140318 | 368 | 0.0216629 | 3.158869e-01 | 1.725906 | 1.826421 | 1.724283 | 1.766308 |
| USDJPY | gjrGARCH | 0.0050025 | 544 | 0.0146875 | 1.890876e-01 | 1.701917 | 1.802973 | 1.700295 | 1.742536 |
| USDJPY | apARCH | 0.4636178 | 80 | 0.0884096 | 8.902071e+04 | -63.693420 | -63.561479 | -63.696159 | -63.640390 |
| USDJPY | iGARCH | 0.0097896 | 544 | 0.0146699 | 1.754192e-01 | 1.716428 | 1.790199 | 1.715519 | 1.746080 |
| USDJPY | csGARCH | 0.0089858 | 544 | 0.0146728 | 1.707400e-01 | 1.725512 | 1.840209 | 1.723454 | 1.771614 |
6.2.1.1 : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 0.0014227 | 3808 | 0.0021001 | 11.74735 | -6.443562 | -6.359819 | -6.444690 | -6.409901 |
| fGARCH.GARCH | 0.0013408 | 3808 | 0.0021001 | 11.74715 | -6.443134 | -6.359390 | -6.444261 | -6.409472 |
| fGARCH.TGARCH | 0.0008103 | 3808 | 0.0021004 | 11.76374 | -6.268054 | -6.170663 | -6.269551 | -6.228907 |
| fGARCH.AVGARCH | 0.0263737 | 220 | 0.0361239 | 17.29090 | -6.152041 | -6.039109 | -6.154038 | -6.106648 |
| fGARCH.NGARCH | 0.0017213 | 3808 | 0.0020999 | 5324.20417 | -16.453801 | -16.356410 | -16.455298 | -16.414654 |
| fGARCH.NAGARCH | 0.0007025 | 3808 | 0.0021005 | 26.14899 | -6.329377 | -6.231985 | -6.330873 | -6.290229 |
| fGARCH.APARCH | 0.0019474 | 1252 | 0.0063867 | 7907.45675 | -20.381252 | -20.271184 | -20.383145 | -20.337009 |
| fGARCH.GJRGARCH | 0.0010277 | 3808 | 0.0021003 | 11.77121 | -6.459558 | -6.362166 | -6.461054 | -6.420411 |
| fGARCH.ALLGARCH | 0.0041303 | 1448 | 0.0055192 | 3661.31882 | -13.330792 | -13.206321 | -13.333180 | -13.280759 |
| eGARCH | 0.0020004 | 2584 | 0.0030944 | 13.36216 | -6.583562 | -6.484996 | -6.585102 | -6.543942 |
| gjrGARCH | 0.0007161 | 3808 | 0.0021005 | 11.77320 | -6.473558 | -6.376166 | -6.475054 | -6.434411 |
| apARCH | 0.0657633 | 564 | 0.0139512 | 13005.71625 | -15.856687 | -15.745559 | -15.858622 | -15.812019 |
| iGARCH | 0.0014003 | 3808 | 0.0021001 | 11.74278 | -6.439027 | -6.368932 | -6.439838 | -6.410852 |
| csGARCH | 0.0012859 | 3808 | 0.0021002 | 11.72541 | -6.432383 | -6.321343 | -6.434301 | -6.387749 |
6.2.1.2 : Table summary
| Model | n |
|---|---|
| fGARCH.TGARCH | 3 |
| fGARCH.AVGARCH | 1 |
| fGARCH.NGARCH | 8 |
| fGARCH.NAGARCH | 5 |
| fGARCH.ALLGARCH | 4 |
| eGARCH | 1 |
| apARCH | 1 |
| csGARCH | 1 |
6.2.1.3 : Table summary
## selected models' filtered closing price.
op <- united.fx2 %>%
separate(Type, c('Cur', 'Type')) %>%
dplyr::filter(Type == 'Op') %>% dplyr::select(-Cur, -Type)
acc <- op %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 1.100000e-06 | 559 | 1.431130e-02 | 0.1475105 | -7.275622 | -7.193904 | -7.276690 | -7.242774 |
| USDAUD | fGARCH.GARCH | 1.100000e-06 | 559 | 1.431130e-02 | 0.1472847 | -7.275369 | -7.193651 | -7.276437 | -7.242522 |
| USDAUD | fGARCH.TGARCH | 9.977529e+00 | 559 | -2.138650e-02 | 2.2663354 | -7.043007 | -6.947635 | -7.044436 | -7.004671 |
| USDAUD | fGARCH.NGARCH | 3.606767e+15 | 559 | -1.290435e+13 | 5134.5786350 | -16.654030 | -16.558658 | -16.655460 | -16.615695 |
| USDAUD | fGARCH.NAGARCH | 1.656780e+61 | 559 | -5.927656e+58 | 67.6839465 | -6.802571 | -6.707200 | -6.804001 | -6.764236 |
| USDAUD | fGARCH.GJRGARCH | 1.000000e-06 | 559 | 1.431130e-02 | 0.1499755 | -7.279926 | -7.184554 | -7.281356 | -7.241590 |
| USDAUD | gjrGARCH | 1.000000e-06 | 559 | 1.431130e-02 | 0.1524026 | -7.287664 | -7.192292 | -7.289093 | -7.249328 |
| USDAUD | iGARCH | 1.100000e-06 | 559 | 1.431130e-02 | 0.1467011 | -7.280357 | -7.212292 | -7.281117 | -7.252997 |
| USDAUD | csGARCH | 1.300000e-06 | 559 | 1.431130e-02 | 0.1507580 | -7.256958 | -7.147932 | -7.258802 | -7.213133 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 4.000000e-07 | 559 | 1.431130e-02 | 0.3231024 | -8.260904 | -8.177451 | -8.262010 | -8.227360 |
| USDEUR | fGARCH.GARCH | 4.000000e-07 | 559 | 1.431130e-02 | 0.3231340 | -8.260830 | -8.177377 | -8.261936 | -8.227286 |
| USDEUR | fGARCH.TGARCH | 6.000000e-07 | 559 | 1.431130e-02 | 0.5406883 | -8.136113 | -8.039007 | -8.137587 | -8.097080 |
| USDEUR | fGARCH.NGARCH | 1.000000e-06 | 559 | 1.431130e-02 | 4635.7699223 | -15.197491 | -15.100385 | -15.198966 | -15.158458 |
| USDEUR | fGARCH.NAGARCH | 4.000000e-07 | 559 | 1.431130e-02 | 0.3283555 | -8.267473 | -8.170366 | -8.268947 | -8.228440 |
| USDEUR | fGARCH.GJRGARCH | 3.000000e-07 | 559 | 1.431130e-02 | 0.3307474 | -8.271118 | -8.174011 | -8.272592 | -8.232084 |
| USDEUR | gjrGARCH | 3.000000e-07 | 559 | 1.431130e-02 | 0.3354663 | -8.286157 | -8.189051 | -8.287631 | -8.247124 |
| USDEUR | iGARCH | 4.000000e-07 | 559 | 1.431130e-02 | 0.3275217 | -8.259763 | -8.189963 | -8.260553 | -8.231706 |
| USDEUR | csGARCH | 5.000000e-07 | 559 | 1.431130e-02 | 0.3204142 | -8.239874 | -8.129114 | -8.241769 | -8.195352 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 0.1028412 | -8.970168 | -8.885417 | -8.971342 | -8.936103 |
| USDGBP | fGARCH.GARCH | 1.000000e-07 | 559 | 1.431130e-02 | 0.1028402 | -8.970515 | -8.885763 | -8.971689 | -8.936449 |
| USDGBP | fGARCH.TGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 0.5417127 | -8.667962 | -8.569570 | -8.669507 | -8.628413 |
| USDGBP | fGARCH.NGARCH | 4.513340e+70 | 559 | -1.614791e+68 | 5079.0448215 | -17.782959 | -17.684567 | -17.784505 | -17.743410 |
| USDGBP | fGARCH.NAGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 26.6382034 | -8.763450 | -8.665059 | -8.764996 | -8.723902 |
| USDGBP | fGARCH.GJRGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 0.1081367 | -8.982733 | -8.884342 | -8.984279 | -8.943185 |
| USDGBP | gjrGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 0.1116630 | -8.996274 | -8.897882 | -8.997820 | -8.956726 |
| USDGBP | iGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 0.1025959 | -8.970351 | -8.899239 | -8.971205 | -8.941767 |
| USDGBP | csGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 0.1014585 | -8.949646 | -8.837615 | -8.951617 | -8.904616 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 3.800000e-06 | 559 | 1.431130e-02 | 0.4886477 | -7.476419 | -7.394283 | -7.477510 | -7.443403 |
| USDCHF | fGARCH.GARCH | 3.800000e-06 | 559 | 1.431130e-02 | 0.4901544 | -7.474242 | -7.392106 | -7.475333 | -7.441226 |
| USDCHF | fGARCH.TGARCH | 7.900000e-06 | 559 | 1.431120e-02 | 1.2621200 | -7.434674 | -7.338882 | -7.436128 | -7.396169 |
| USDCHF | fGARCH.NGARCH | 4.064080e-02 | 559 | 1.416590e-02 | 7157.3626097 | -24.381321 | -24.285530 | -24.382776 | -24.342816 |
| USDCHF | fGARCH.NAGARCH | 8.620427e+287 | 559 | -3.084232e+285 | 1236.5953284 | -4.688806 | -4.593014 | -4.690260 | -4.650301 |
| USDCHF | fGARCH.GJRGARCH | 2.300000e-06 | 559 | 1.431130e-02 | 0.4587686 | -7.519756 | -7.423965 | -7.521210 | -7.481251 |
| USDCHF | gjrGARCH | 2.300000e-06 | 559 | 1.431130e-02 | 0.4555439 | -7.546330 | -7.450539 | -7.547784 | -7.507825 |
| USDCHF | iGARCH | 3.700000e-06 | 559 | 1.431130e-02 | 0.5429386 | -7.452233 | -7.383753 | -7.453014 | -7.424706 |
| USDCHF | csGARCH | 3.700000e-06 | 559 | 1.431130e-02 | 0.4952953 | -7.457041 | -7.347594 | -7.458911 | -7.413047 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 0.1828809 | -7.978945 | -7.898882 | -7.979974 | -7.946763 |
| USDCAD | fGARCH.GARCH | 3.000000e-07 | 559 | 1.431130e-02 | 0.1827221 | -7.979083 | -7.899020 | -7.980112 | -7.946901 |
| USDCAD | fGARCH.TGARCH | 8.000000e-07 | 559 | 1.431130e-02 | 0.4607513 | -7.778762 | -7.685046 | -7.780146 | -7.741092 |
| USDCAD | fGARCH.NGARCH | 7.000000e-07 | 559 | 1.431130e-02 | 3587.1678042 | -13.910234 | -13.816518 | -13.911618 | -13.872564 |
| USDCAD | fGARCH.NAGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 0.1822239 | -7.986122 | -7.892406 | -7.987507 | -7.948452 |
| USDCAD | fGARCH.GJRGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 0.1864332 | -7.985711 | -7.891995 | -7.987095 | -7.948040 |
| USDCAD | gjrGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 0.1846478 | -7.992367 | -7.898651 | -7.993751 | -7.954697 |
| USDCAD | iGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 0.1856758 | -7.976740 | -7.910331 | -7.977467 | -7.950046 |
| USDCAD | csGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 0.1795049 | -7.963757 | -7.856388 | -7.965549 | -7.920598 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 7.200000e-06 | 559 | 1.431120e-02 | 0.1978232 | -6.862343 | -6.774548 | -6.863560 | -6.827053 |
| USDCNY | fGARCH.GARCH | 7.100000e-06 | 559 | 1.431120e-02 | 0.1976357 | -6.861473 | -6.773677 | -6.862690 | -6.826183 |
| USDCNY | fGARCH.TGARCH | 5.366621e+04 | 559 | -1.919936e+02 | 9.3556676 | -6.380259 | -6.278821 | -6.381861 | -6.339486 |
| USDCNY | fGARCH.NGARCH | 9.000000e-06 | 559 | 1.431120e-02 | 3052.2188213 | -12.142771 | -12.041334 | -12.144374 | -12.101998 |
| USDCNY | fGARCH.NAGARCH | 6.500000e-06 | 559 | 1.431120e-02 | 0.1907778 | -6.897824 | -6.796386 | -6.899426 | -6.857051 |
| USDCNY | fGARCH.GJRGARCH | 7.200000e-06 | 559 | 1.431120e-02 | 0.1869098 | -6.894584 | -6.793146 | -6.896186 | -6.853811 |
| USDCNY | gjrGARCH | 7.900000e-06 | 559 | 1.431120e-02 | 0.1766534 | -6.910032 | -6.808594 | -6.911634 | -6.869259 |
| USDCNY | iGARCH | 8.300000e-06 | 559 | 1.431120e-02 | 0.2034711 | -6.851271 | -6.777118 | -6.852157 | -6.821465 |
| USDCNY | csGARCH | 1.060000e-05 | 559 | 1.431120e-02 | 0.2116209 | -6.884467 | -6.769387 | -6.886507 | -6.838210 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 9.769800e-03 | 559 | 1.427630e-02 | 0.1736917 | 1.721961 | 1.809420 | 1.720719 | 1.757115 |
| USDJPY | fGARCH.GARCH | 9.273200e-03 | 559 | 1.427810e-02 | 0.1737364 | 1.721989 | 1.809449 | 1.720747 | 1.757143 |
| USDJPY | fGARCH.TGARCH | 4.865454e+176 | 559 | -1.740771e+174 | 333.4709800 | 2.502594 | 2.603697 | 2.500970 | 2.543232 |
| USDJPY | fGARCH.NGARCH | 1.185840e-02 | 559 | 1.426880e-02 | 9255.6562217 | -16.887684 | -16.786582 | -16.889309 | -16.847046 |
| USDJPY | fGARCH.NAGARCH | 4.822900e-03 | 559 | 1.429400e-02 | 0.1846586 | 1.709179 | 1.810281 | 1.707554 | 1.749817 |
| USDJPY | fGARCH.GJRGARCH | 7.071700e-03 | 559 | 1.428600e-02 | 0.1801842 | 1.718061 | 1.819164 | 1.716436 | 1.758699 |
| USDJPY | gjrGARCH | 4.906300e-03 | 559 | 1.429370e-02 | 0.1887046 | 1.705786 | 1.806888 | 1.704161 | 1.746424 |
| USDJPY | iGARCH | 9.597700e-03 | 559 | 1.427690e-02 | 0.1755607 | 1.719560 | 1.793377 | 1.718648 | 1.749230 |
| USDJPY | csGARCH | 8.935700e-03 | 559 | 1.427930e-02 | 0.1705228 | 1.729581 | 1.844326 | 1.727521 | 1.775703 |
6.2.2.1A : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 1.397500e-03 | 3913 | 2.043800e-03 | 11.75295 | -6.443206 | -6.359295 | -6.444338 | -6.409477 |
| fGARCH.GARCH | 1.326600e-03 | 3913 | 2.043800e-03 | 11.75262 | -6.442789 | -6.358878 | -6.443921 | -6.409061 |
| fGARCH.TGARCH | 6.950648e+175 | 3913 | -3.552593e+172 | 62.60034 | -6.134026 | -6.036466 | -6.135528 | -6.094811 |
| fGARCH.NGARCH | 6.447629e+69 | 3913 | -3.295491e+66 | 5427.54570 | -16.708070 | -16.610511 | -16.709572 | -16.668855 |
| fGARCH.NAGARCH | 1.231490e+287 | 3913 | -6.294350e+283 | 201.58772 | -5.956724 | -5.859164 | -5.958226 | -5.917509 |
| fGARCH.GJRGARCH | 1.011800e-03 | 3913 | 2.043900e-03 | 11.77688 | -6.459395 | -6.361835 | -6.460897 | -6.420180 |
| gjrGARCH | 7.026000e-04 | 3913 | 2.044100e-03 | 11.78104 | -6.473291 | -6.375731 | -6.474793 | -6.434076 |
| iGARCH | 1.373100e-03 | 3913 | 2.043800e-03 | 11.74837 | -6.438736 | -6.368474 | -6.439552 | -6.410494 |
| csGARCH | 1.278900e-03 | 3913 | 2.043800e-03 | 11.73289 | -6.431737 | -6.320529 | -6.433662 | -6.387036 |
6.2.2.1B : Table summary
| Model | n |
|---|---|
| fGARCH.TGARCH | 3 |
| fGARCH.NGARCH | 4 |
| fGARCH.NAGARCH | 4 |
6.2.2.1C : Table summary
## selected models' filtered closing price.
op <- united.fx3 %>%
separate(Type, c('Cur', 'Type')) %>%
dplyr::filter(Type == 'Op') %>% dplyr::select(-Cur, -Type)
acc <- op %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 0.0000010 | 488 | 0.0163934 | 1.556138e-01 | -7.254120 | -7.173213 | -7.255161 | -7.221598 |
| USDAUD | fGARCH.GARCH | 0.0000010 | 488 | 0.0163934 | 1.553627e-01 | -7.253888 | -7.172981 | -7.254929 | -7.221366 |
| USDAUD | fGARCH.TGARCH | 0.0000029 | 488 | 0.0163934 | 4.679305e-01 | -7.074004 | -6.979445 | -7.075405 | -7.035995 |
| USDAUD | fGARCH.NGARCH | 0.0000044 | 488 | 0.0163934 | 4.857513e+03 | -16.076598 | -15.982038 | -16.077998 | -16.038588 |
| USDAUD | fGARCH.NAGARCH | 0.0000009 | 488 | 0.0163934 | 1.627755e-01 | -7.264740 | -7.170180 | -7.266140 | -7.226730 |
| USDAUD | fGARCH.GJRGARCH | 0.0000010 | 488 | 0.0163934 | 1.580248e-01 | -7.258031 | -7.163471 | -7.259431 | -7.220021 |
| USDAUD | gjrGARCH | 0.0000009 | 488 | 0.0163934 | 1.606617e-01 | -7.265726 | -7.171166 | -7.267126 | -7.227717 |
| USDAUD | iGARCH | 0.0000010 | 488 | 0.0163934 | 1.546628e-01 | -7.258773 | -7.191520 | -7.259510 | -7.231740 |
| USDAUD | csGARCH | 0.0000013 | 488 | 0.0163934 | 1.586854e-01 | -7.236336 | -7.128123 | -7.238148 | -7.192838 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 0.0000004 | 488 | 0.0163934 | 2.900517e-01 | -8.191259 | -8.108169 | -8.192355 | -8.157860 |
| USDEUR | fGARCH.GARCH | 0.0000003 | 488 | 0.0163934 | 2.900111e-01 | -8.191161 | -8.108072 | -8.192257 | -8.157762 |
| USDEUR | fGARCH.TGARCH | 0.0000006 | 488 | 0.0163934 | 5.218764e-01 | -8.060845 | -7.964103 | -8.062309 | -8.021959 |
| USDEUR | fGARCH.NGARCH | 0.0000010 | 488 | 0.0163934 | 4.630143e+03 | -14.947687 | -14.850944 | -14.949150 | -14.908800 |
| USDEUR | fGARCH.NAGARCH | 0.0000003 | 488 | 0.0163934 | 2.967079e-01 | -8.198668 | -8.101925 | -8.200131 | -8.159781 |
| USDEUR | fGARCH.GJRGARCH | 0.0000003 | 488 | 0.0163934 | 3.002674e-01 | -8.202633 | -8.105890 | -8.204096 | -8.163746 |
| USDEUR | gjrGARCH | 0.0000003 | 488 | 0.0163934 | 3.069921e-01 | -8.218761 | -8.122018 | -8.220224 | -8.179874 |
| USDEUR | iGARCH | 0.0000004 | 488 | 0.0163934 | 2.947628e-01 | -8.189928 | -8.120492 | -8.190711 | -8.162017 |
| USDEUR | csGARCH | 0.0000005 | 488 | 0.0163934 | 2.869198e-01 | -8.169529 | -8.059132 | -8.171412 | -8.125153 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 0.0000001 | 488 | 0.0163934 | 9.119210e-02 | -8.928410 | -8.844473 | -8.929560 | -8.894671 |
| USDGBP | fGARCH.GARCH | 0.0000001 | 488 | 0.0163934 | 9.098120e-02 | -8.928492 | -8.844555 | -8.929643 | -8.894754 |
| USDGBP | fGARCH.TGARCH | 0.0000002 | 488 | 0.0163934 | 5.411907e-01 | -8.624873 | -8.527298 | -8.626393 | -8.585653 |
| USDGBP | fGARCH.NGARCH | 0.0000002 | 488 | 0.0163934 | 4.713194e+03 | -16.885314 | -16.787739 | -16.886834 | -16.846094 |
| USDGBP | fGARCH.NAGARCH | 0.0000001 | 488 | 0.0163934 | 3.045887e+01 | -8.690217 | -8.592641 | -8.691737 | -8.650997 |
| USDGBP | fGARCH.GJRGARCH | 0.0000002 | 488 | 0.0163934 | 9.672370e-02 | -8.940411 | -8.842835 | -8.941931 | -8.901190 |
| USDGBP | gjrGARCH | 0.0000001 | 488 | 0.0163934 | 1.005950e-01 | -8.953914 | -8.856338 | -8.955434 | -8.914694 |
| USDGBP | iGARCH | 0.0000001 | 488 | 0.0163934 | 9.146430e-02 | -8.928891 | -8.858593 | -8.929726 | -8.900635 |
| USDGBP | csGARCH | 0.0000001 | 488 | 0.0163934 | 8.998960e-02 | -8.909204 | -8.797990 | -8.911146 | -8.864502 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 0.0000041 | 488 | 0.0163934 | 4.486903e-01 | -7.427126 | -7.345576 | -7.428195 | -7.394346 |
| USDCHF | fGARCH.GARCH | 0.0000040 | 488 | 0.0163934 | 4.498492e-01 | -7.424633 | -7.343083 | -7.425702 | -7.391853 |
| USDCHF | fGARCH.TGARCH | 0.0000090 | 488 | 0.0163934 | 1.352756e+00 | -7.365038 | -7.269832 | -7.366468 | -7.326768 |
| USDCHF | fGARCH.NGARCH | 0.0000029 | 488 | 0.0163934 | 6.783309e+03 | -23.088317 | -22.993112 | -23.089748 | -23.050048 |
| USDCHF | fGARCH.NAGARCH | 0.0000020 | 488 | 0.0163934 | 8.447514e+01 | -6.702795 | -6.607589 | -6.704225 | -6.664525 |
| USDCHF | fGARCH.GJRGARCH | 0.0000025 | 488 | 0.0163934 | 4.248092e-01 | -7.470917 | -7.375712 | -7.472348 | -7.432648 |
| USDCHF | gjrGARCH | 0.0000025 | 488 | 0.0163934 | 4.277950e-01 | -7.494131 | -7.398926 | -7.495562 | -7.455862 |
| USDCHF | iGARCH | 0.0000040 | 488 | 0.0163934 | 5.033615e-01 | -7.401239 | -7.333345 | -7.402000 | -7.373948 |
| USDCHF | csGARCH | 0.0000040 | 488 | 0.0163934 | 4.550693e-01 | -7.407634 | -7.298772 | -7.409478 | -7.363875 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 0.0000002 | 488 | 0.0163934 | 1.886554e-01 | -7.953760 | -7.873799 | -7.954785 | -7.921619 |
| USDCAD | fGARCH.GARCH | 0.0000002 | 488 | 0.0163934 | 1.885970e-01 | -7.954064 | -7.874103 | -7.955089 | -7.921923 |
| USDCAD | fGARCH.TGARCH | 0.0000009 | 488 | 0.0163934 | 4.801332e-01 | -7.739545 | -7.645931 | -7.740925 | -7.701915 |
| USDCAD | fGARCH.NGARCH | 0.0000005 | 488 | 0.0163934 | 2.699000e+03 | -12.562075 | -12.468460 | -12.563454 | -12.524445 |
| USDCAD | fGARCH.NAGARCH | 0.0000002 | 488 | 0.0163934 | 1.884552e-01 | -7.961253 | -7.867638 | -7.962632 | -7.923623 |
| USDCAD | fGARCH.GJRGARCH | 0.0000002 | 488 | 0.0163934 | 1.931320e-01 | -7.961379 | -7.867765 | -7.962759 | -7.923749 |
| USDCAD | gjrGARCH | 0.0000002 | 488 | 0.0163934 | 1.907231e-01 | -7.967757 | -7.874143 | -7.969137 | -7.930128 |
| USDCAD | iGARCH | 0.0000002 | 488 | 0.0163934 | 1.921708e-01 | -7.951811 | -7.885503 | -7.952534 | -7.925158 |
| USDCAD | csGARCH | 0.0000002 | 488 | 0.0163934 | 1.855792e-01 | -7.939182 | -7.831915 | -7.940970 | -7.896065 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 0.0000074 | 488 | 0.0163934 | 1.758498e-01 | -6.810419 | -6.722578 | -6.811638 | -6.775111 |
| USDCNY | fGARCH.GARCH | 0.0000073 | 488 | 0.0163934 | 1.755708e-01 | -6.809793 | -6.721953 | -6.811012 | -6.774486 |
| USDCNY | fGARCH.TGARCH | 0.0000169 | 488 | 0.0163934 | 1.468451e+00 | -6.461091 | -6.359609 | -6.462695 | -6.420300 |
| USDCNY | fGARCH.NGARCH | 0.0000088 | 488 | 0.0163934 | 3.492262e+03 | -12.855476 | -12.753994 | -12.857080 | -12.814685 |
| USDCNY | fGARCH.NAGARCH | 0.0000070 | 488 | 0.0163934 | 1.699647e-01 | -6.848156 | -6.746674 | -6.849760 | -6.807365 |
| USDCNY | fGARCH.GJRGARCH | 0.0000077 | 488 | 0.0163934 | 1.665611e-01 | -6.846045 | -6.744563 | -6.847649 | -6.805255 |
| USDCNY | gjrGARCH | 0.0000085 | 488 | 0.0163934 | 1.569713e-01 | -6.862203 | -6.760721 | -6.863807 | -6.821412 |
| USDCNY | iGARCH | 0.0000087 | 488 | 0.0163934 | 1.799151e-01 | -6.798577 | -6.724378 | -6.799464 | -6.768753 |
| USDCNY | csGARCH | 0.0000113 | 488 | 0.0163934 | 1.878565e-01 | -6.832669 | -6.717545 | -6.834710 | -6.786395 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 0.0104083 | 488 | 0.0163508 | 1.675998e-01 | 1.765236 | 1.851882 | 1.764017 | 1.800063 |
| USDJPY | fGARCH.GARCH | 0.0098588 | 488 | 0.0163530 | 1.676050e-01 | 1.765304 | 1.851950 | 1.764085 | 1.800131 |
| USDJPY | fGARCH.TGARCH | 0.0235432 | 488 | 0.0162970 | 1.788881e-01 | 1.770424 | 1.870711 | 1.768825 | 1.810734 |
| USDJPY | fGARCH.NGARCH | 0.0126471 | 488 | 0.0163416 | 1.027431e+04 | -18.759773 | -18.659485 | -18.761372 | -18.719463 |
| USDJPY | fGARCH.NAGARCH | 0.0050057 | 488 | 0.0163729 | 1.788160e-01 | 1.753070 | 1.853358 | 1.751472 | 1.793380 |
| USDJPY | fGARCH.GJRGARCH | 0.0072613 | 488 | 0.0163637 | 1.738160e-01 | 1.761961 | 1.862249 | 1.760363 | 1.802272 |
| USDJPY | gjrGARCH | 0.0051751 | 488 | 0.0163722 | 1.820482e-01 | 1.750468 | 1.850755 | 1.748869 | 1.790778 |
| USDJPY | iGARCH | 0.0102762 | 488 | 0.0163513 | 1.690952e-01 | 1.763320 | 1.836325 | 1.762428 | 1.792664 |
| USDJPY | csGARCH | 0.0094768 | 488 | 0.0163546 | 1.642400e-01 | 1.772853 | 1.886782 | 1.770822 | 1.818646 |
6.2.2.2A : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 0.0014888 | 3416 | 0.0023410 | 11.73676 | -6.399980 | -6.316561 | -6.401097 | -6.366449 |
| fGARCH.GARCH | 0.0014103 | 3416 | 0.0023411 | 11.73625 | -6.399533 | -6.316114 | -6.400650 | -6.366002 |
| fGARCH.TGARCH | 0.0033677 | 3416 | 0.0023399 | 11.77682 | -6.222139 | -6.125072 | -6.223624 | -6.183122 |
| fGARCH.NGARCH | 0.0018093 | 3416 | 0.0023409 | 5361.39348 | -16.453606 | -16.356539 | -16.455091 | -16.414589 |
| fGARCH.NAGARCH | 0.0007166 | 3416 | 0.0023415 | 27.74985 | -6.273251 | -6.176184 | -6.274736 | -6.234235 |
| fGARCH.GJRGARCH | 0.0010390 | 3416 | 0.0023413 | 11.76458 | -6.416779 | -6.319712 | -6.418265 | -6.377763 |
| gjrGARCH | 0.0007411 | 3416 | 0.0023415 | 11.77114 | -6.430289 | -6.333222 | -6.431774 | -6.391273 |
| iGARCH | 0.0014701 | 3416 | 0.0023411 | 11.73302 | -6.395128 | -6.325358 | -6.395931 | -6.367084 |
| csGARCH | 0.0013563 | 3416 | 0.0023411 | 11.71734 | -6.388814 | -6.278099 | -6.390720 | -6.344312 |
6.2.2.2B : Table summary
| Model | n |
|---|---|
6.2.2.2C : Table summary
## filtered bias highest price.
hp <- fx %>% separate(Type, c('Cur', 'Type')) %>%
dplyr::filter(Type == 'Hi') %>%
dplyr::select(-Cur, -Type)
ntmID <- hp %>% dplyr::filter(se == 1) %>% .$Date %>% unlist %>% sort
acc <- hp %>% dplyr::filter(!Date %in% ntmID & Date %in% ntimeID2) %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 0.0000003 | 540 | 0.0148148 | 1.512588e-01 | -7.429445 | -7.351779 | -7.430408 | -7.398226 |
| USDAUD | fGARCH.GARCH | 0.0000003 | 540 | 0.0148148 | 1.511517e-01 | -7.429667 | -7.352002 | -7.430630 | -7.398449 |
| USDAUD | fGARCH.TGARCH | 0.0000037 | 540 | 0.0148148 | 7.181205e-01 | -7.128276 | -7.036957 | -7.129584 | -7.091569 |
| USDAUD | fGARCH.AVGARCH | 0.0000000 | 52 | 0.1538462 | 7.201320e-02 | -7.670617 | -7.571365 | -7.672139 | -7.630722 |
| USDAUD | fGARCH.NGARCH | 0.0000006 | 540 | 0.0148148 | 1.021187e+03 | -7.260611 | -7.169293 | -7.261920 | -7.223905 |
| USDAUD | fGARCH.NAGARCH | 0.0000002 | 540 | 0.0148148 | 1.571420e-01 | -7.442532 | -7.351214 | -7.443841 | -7.405825 |
| USDAUD | fGARCH.APARCH | 0.0000061 | 208 | 0.0384615 | 6.555577e+03 | -18.348660 | -18.242280 | -18.350412 | -18.305897 |
| USDAUD | fGARCH.GJRGARCH | 0.0000002 | 540 | 0.0148148 | 1.550220e-01 | -7.429825 | -7.338507 | -7.431134 | -7.393118 |
| USDAUD | fGARCH.ALLGARCH | 0.0000002 | 115 | 0.0695652 | 5.187800e-02 | -7.756351 | -7.636859 | -7.758552 | -7.708319 |
| USDAUD | eGARCH | 0.0000002 | 364 | 0.0219780 | 9.778890e-02 | -7.574364 | -7.482161 | -7.575697 | -7.537301 |
| USDAUD | gjrGARCH | 0.0000002 | 540 | 0.0148148 | 1.575609e-01 | -7.436966 | -7.345648 | -7.438274 | -7.400259 |
| USDAUD | apARCH | 0.0000004 | 78 | 0.1025641 | 4.423700e-03 | -7.870832 | -7.767356 | -7.872499 | -7.829238 |
| USDAUD | iGARCH | 0.0000003 | 540 | 0.0148148 | 1.513257e-01 | -7.431959 | -7.367947 | -7.432630 | -7.406229 |
| USDAUD | csGARCH | 0.0000003 | 540 | 0.0148148 | 1.506154e-01 | -7.415393 | -7.310422 | -7.417101 | -7.373199 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 0.0000008 | 540 | 0.0148148 | 2.782775e-01 | -8.493735 | -8.410816 | -8.494827 | -8.460405 |
| USDEUR | fGARCH.GARCH | 0.0000008 | 540 | 0.0148148 | 2.766654e-01 | -8.494266 | -8.411346 | -8.495358 | -8.460935 |
| USDEUR | fGARCH.TGARCH | 0.0000019 | 540 | 0.0148148 | 3.566665e-01 | -8.349335 | -8.252762 | -8.350793 | -8.310516 |
| USDEUR | fGARCH.AVGARCH | 0.0000003 | 27 | 0.2962963 | 3.179274e-01 | -7.954440 | -7.834094 | -7.956648 | -7.906065 |
| USDEUR | fGARCH.NGARCH | 0.0000013 | 540 | 0.0148148 | 7.274670e+03 | -21.236805 | -21.140233 | -21.238264 | -21.197987 |
| USDEUR | fGARCH.NAGARCH | 0.0000007 | 540 | 0.0148148 | 2.782084e-01 | -8.493455 | -8.396883 | -8.494914 | -8.454637 |
| USDEUR | fGARCH.APARCH | 0.0000002 | 88 | 0.0909091 | 2.825180e-01 | -8.083915 | -7.965181 | -8.086085 | -8.036188 |
| USDEUR | fGARCH.GJRGARCH | 0.0000007 | 540 | 0.0148148 | 2.744882e-01 | -8.493588 | -8.397016 | -8.495047 | -8.454770 |
| USDEUR | fGARCH.ALLGARCH | 0.0000001 | 221 | 0.0361991 | 8.518890e-02 | -8.423827 | -8.303298 | -8.426061 | -8.375377 |
| USDEUR | eGARCH | 0.0000002 | 366 | 0.0218579 | 1.620773e-01 | -8.712223 | -8.617503 | -8.713637 | -8.674148 |
| USDEUR | gjrGARCH | 0.0000007 | 540 | 0.0148148 | 2.626868e-01 | -8.516242 | -8.419670 | -8.517701 | -8.477424 |
| USDEUR | apARCH | 0.0000002 | 78 | 0.1025641 | 1.382580e-01 | -8.168651 | -8.048534 | -8.170867 | -8.120368 |
| USDEUR | iGARCH | 0.0000008 | 540 | 0.0148148 | 2.709582e-01 | -8.492762 | -8.423495 | -8.493541 | -8.464920 |
| USDEUR | csGARCH | 0.0000007 | 540 | 0.0148148 | 2.319467e-01 | -8.495272 | -8.385047 | -8.497150 | -8.450966 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 0.0000001 | 540 | 0.0148148 | 1.290413e-01 | -9.102697 | -9.018870 | -9.103839 | -9.069003 |
| USDGBP | fGARCH.GARCH | 0.0000001 | 540 | 0.0148148 | 1.289423e-01 | -9.102752 | -9.018925 | -9.103894 | -9.069058 |
| USDGBP | fGARCH.TGARCH | 0.0000004 | 540 | 0.0148148 | 7.297310e-01 | -8.781872 | -8.684405 | -8.783382 | -8.742696 |
| USDGBP | fGARCH.AVGARCH | 0.0000000 | 34 | 0.2352941 | 1.576003e+02 | -6.569828 | -6.468899 | -6.571394 | -6.529263 |
| USDGBP | fGARCH.NGARCH | 0.0000002 | 540 | 0.0148148 | 1.164599e+03 | -9.742275 | -9.644808 | -9.743785 | -9.703099 |
| USDGBP | fGARCH.NAGARCH | 0.0000001 | 540 | 0.0148148 | 1.486233e+02 | -8.403556 | -8.306089 | -8.405066 | -8.364380 |
| USDGBP | fGARCH.APARCH | 0.0000002 | 208 | 0.0384615 | 9.439821e+02 | -12.369332 | -12.267555 | -12.370939 | -12.328423 |
| USDGBP | fGARCH.GJRGARCH | 0.0000001 | 540 | 0.0148148 | 1.302802e-01 | -9.113103 | -9.015636 | -9.114613 | -9.073926 |
| USDGBP | fGARCH.ALLGARCH | 0.0000000 | 222 | 0.0360360 | 1.885192e+03 | -13.098373 | -12.983155 | -13.100410 | -13.052061 |
| USDGBP | eGARCH | 0.0000001 | 365 | 0.0219178 | 9.014454e+00 | -9.036373 | -8.942729 | -9.037766 | -8.998732 |
| USDGBP | gjrGARCH | 0.0000001 | 540 | 0.0148148 | 1.090160e-01 | -9.129492 | -9.032026 | -9.131003 | -9.090316 |
| USDGBP | apARCH | 0.0000003 | 78 | 0.1025641 | 2.134324e-01 | -8.949299 | -8.842622 | -8.951082 | -8.906423 |
| USDGBP | iGARCH | 0.0000001 | 540 | 0.0148148 | 1.297254e-01 | -9.102258 | -9.032071 | -9.103084 | -9.074047 |
| USDGBP | csGARCH | 0.0000001 | 540 | 0.0148148 | 7.837160e-02 | -9.102038 | -8.990932 | -9.103970 | -9.057380 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 0.0000031 | 540 | 0.0148148 | 4.454097e-01 | -7.666875 | -7.584531 | -7.667952 | -7.633775 |
| USDCHF | fGARCH.GARCH | 0.0000031 | 540 | 0.0148148 | 4.451960e-01 | -7.666643 | -7.584299 | -7.667720 | -7.633543 |
| USDCHF | fGARCH.TGARCH | 0.0000004 | 540 | 0.0148148 | 2.862227e-01 | -7.705898 | -7.609899 | -7.707340 | -7.667310 |
| USDCHF | fGARCH.AVGARCH | 0.0000003 | 16 | 0.5000000 | 2.317470e-02 | -7.934905 | -7.820994 | -7.936898 | -7.889110 |
| USDCHF | fGARCH.NGARCH | 0.0000023 | 540 | 0.0148148 | 1.501212e+03 | -10.107112 | -10.011113 | -10.108554 | -10.068523 |
| USDCHF | fGARCH.NAGARCH | 0.0000015 | 540 | 0.0148148 | 1.463865e+02 | -6.759104 | -6.663105 | -6.760546 | -6.720515 |
| USDCHF | fGARCH.APARCH | 0.0000003 | 207 | 0.0386473 | 1.692811e+03 | -11.019402 | -10.903272 | -11.021480 | -10.972719 |
| USDCHF | fGARCH.GJRGARCH | 0.0000019 | 540 | 0.0148148 | 4.157231e-01 | -7.692028 | -7.596030 | -7.693471 | -7.653440 |
| USDCHF | fGARCH.ALLGARCH | 0.0000004 | 221 | 0.0361991 | 7.915994e+03 | -19.588249 | -19.459558 | -19.590781 | -19.536517 |
| USDCHF | eGARCH | 0.0000003 | 365 | 0.0219178 | 1.615499e+00 | -8.050789 | -7.952857 | -8.052294 | -8.011422 |
| USDCHF | gjrGARCH | 0.0000019 | 540 | 0.0148148 | 4.259938e-01 | -7.717160 | -7.621161 | -7.718602 | -7.678572 |
| USDCHF | apARCH | 0.0000002 | 77 | 0.1038961 | 2.281800e-03 | -8.002846 | -7.893448 | -8.004684 | -7.958869 |
| USDCHF | iGARCH | 0.0000031 | 540 | 0.0148148 | 4.874789e-01 | -7.643631 | -7.574943 | -7.644399 | -7.616021 |
| USDCHF | csGARCH | 0.0000031 | 540 | 0.0148148 | 4.496327e-01 | -7.643246 | -7.533592 | -7.645105 | -7.599169 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 0.0000009 | 540 | 0.0148148 | 1.546371e-01 | -8.164071 | -8.074228 | -8.165352 | -8.127958 |
| USDCAD | fGARCH.GARCH | 0.0000010 | 540 | 0.0148148 | 1.547434e-01 | -8.164151 | -8.074308 | -8.165433 | -8.128038 |
| USDCAD | fGARCH.TGARCH | 0.0000020 | 540 | 0.0148148 | 9.136364e-01 | -7.920632 | -7.817135 | -7.922306 | -7.879030 |
| USDCAD | fGARCH.AVGARCH | 0.0000000 | 40 | 0.2000000 | 2.232913e+02 | -5.811174 | -5.710815 | -5.812732 | -5.770834 |
| USDCAD | fGARCH.NGARCH | 0.0000261 | 540 | 0.0148147 | 1.602307e+04 | -44.782315 | -44.678818 | -44.783989 | -44.740713 |
| USDCAD | fGARCH.NAGARCH | 0.0000008 | 540 | 0.0148148 | 1.535060e-01 | -8.171390 | -8.067893 | -8.173064 | -8.129788 |
| USDCAD | fGARCH.APARCH | 0.0000008 | 204 | 0.0392157 | 4.969446e+03 | -16.795057 | -16.688391 | -16.796809 | -16.752179 |
| USDCAD | fGARCH.GJRGARCH | 0.0000008 | 540 | 0.0148148 | 1.500438e-01 | -8.163476 | -8.059980 | -8.165151 | -8.121875 |
| USDCAD | fGARCH.ALLGARCH | 0.0000011 | 221 | 0.0361991 | 5.682965e+03 | -19.474474 | -19.353874 | -19.476692 | -19.425995 |
| USDCAD | eGARCH | 0.0000003 | 364 | 0.0219780 | 1.073588e+00 | -8.303581 | -8.206759 | -8.305033 | -8.264661 |
| USDCAD | gjrGARCH | 0.0000008 | 540 | 0.0148148 | 1.473482e-01 | -8.166347 | -8.062851 | -8.168022 | -8.124746 |
| USDCAD | apARCH | 0.0000000 | 77 | 0.1038961 | 4.259800e-03 | -8.394602 | -8.294747 | -8.396137 | -8.354464 |
| USDCAD | iGARCH | 0.0000010 | 540 | 0.0148148 | 1.551537e-01 | -8.165407 | -8.089216 | -8.166348 | -8.134781 |
| USDCAD | csGARCH | 0.0000010 | 540 | 0.0148148 | 1.534976e-01 | -8.147663 | -8.030514 | -8.149783 | -8.100574 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 0.0000610 | 540 | 0.0148146 | 4.558962e-01 | -6.244466 | -6.148786 | -6.245911 | -6.206007 |
| USDCNY | fGARCH.GARCH | 0.0000608 | 540 | 0.0148146 | 4.574555e-01 | -6.243753 | -6.148074 | -6.245198 | -6.205295 |
| USDCNY | fGARCH.TGARCH | 0.0000384 | 540 | 0.0148147 | 2.548976e+00 | -5.882729 | -5.773407 | -5.884589 | -5.838787 |
| USDCNY | fGARCH.AVGARCH | 0.0000002 | 12 | 0.6666666 | 3.333200e-03 | -7.004461 | -6.888806 | -7.006489 | -6.957979 |
| USDCNY | fGARCH.NGARCH | 0.0000639 | 540 | 0.0148146 | 6.330052e+02 | -7.338929 | -7.229607 | -7.340789 | -7.294987 |
| USDCNY | fGARCH.NAGARCH | 0.0000384 | 540 | 0.0148147 | 4.177205e-01 | -6.275604 | -6.166282 | -6.277465 | -6.231662 |
| USDCNY | fGARCH.APARCH | 0.0020699 | 205 | 0.0390042 | 1.280864e+04 | -28.430343 | -28.307694 | -28.432636 | -28.381044 |
| USDCNY | fGARCH.GJRGARCH | 0.0000417 | 540 | 0.0148147 | 4.443042e-01 | -6.255357 | -6.146035 | -6.257218 | -6.211415 |
| USDCNY | fGARCH.ALLGARCH | 0.0001038 | 221 | 0.0361982 | 1.508048e+03 | -8.820804 | -8.684243 | -8.823624 | -8.765913 |
| USDCNY | eGARCH | 0.0000576 | 362 | 0.0220991 | 3.568470e-01 | -5.936986 | -5.826195 | -5.938884 | -5.892453 |
| USDCNY | gjrGARCH | 0.0000352 | 540 | 0.0148147 | 4.643736e-01 | -6.270866 | -6.161544 | -6.272726 | -6.226924 |
| USDCNY | apARCH | 0.0000186 | 78 | 0.1025636 | 4.539200e-02 | -6.861341 | -6.747847 | -6.863298 | -6.815725 |
| USDCNY | iGARCH | 0.0000597 | 540 | 0.0148146 | 4.472033e-01 | -6.230491 | -6.148453 | -6.231573 | -6.197516 |
| USDCNY | csGARCH | 0.0000604 | 540 | 0.0148146 | 4.657353e-01 | -6.235881 | -6.112917 | -6.238209 | -6.186456 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 0.0126884 | 540 | 0.0147678 | 1.342504e-01 | 1.398436 | 1.492340 | 1.397020 | 1.436181 |
| USDJPY | fGARCH.GARCH | 0.0131018 | 540 | 0.0147663 | 1.341802e-01 | 1.398502 | 1.492406 | 1.397086 | 1.436247 |
| USDJPY | fGARCH.TGARCH | 0.0093465 | 540 | 0.0147802 | 1.772753e-01 | 1.426310 | 1.533858 | 1.424487 | 1.469539 |
| USDJPY | fGARCH.AVGARCH | 0.0352913 | 40 | 0.1982354 | 1.330442e-01 | 1.016510 | 1.145209 | 1.013927 | 1.068237 |
| USDJPY | fGARCH.NGARCH | 0.2128104 | 540 | 0.0140266 | 3.185722e+03 | -4.199724 | -4.092177 | -4.201547 | -4.156495 |
| USDJPY | fGARCH.NAGARCH | 0.0099502 | 540 | 0.0147780 | 1.396100e-01 | 1.386971 | 1.494518 | 1.385148 | 1.430200 |
| USDJPY | fGARCH.APARCH | 448.2839484 | 90 | -9.8729766 | 1.501696e+04 | -23.918951 | -23.791220 | -23.921478 | -23.867613 |
| USDJPY | fGARCH.GJRGARCH | 0.0109226 | 540 | 0.0147744 | 1.361793e-01 | 1.394400 | 1.501947 | 1.392576 | 1.437628 |
| USDJPY | fGARCH.ALLGARCH | 0.3010558 | 192 | 0.0385307 | 1.087965e+02 | 2.000910 | 2.142996 | 1.997817 | 2.058021 |
| USDJPY | eGARCH | 0.0243326 | 363 | 0.0219045 | 1.363897e+00 | 1.481348 | 1.592083 | 1.479403 | 1.525858 |
| USDJPY | gjrGARCH | 0.0111579 | 540 | 0.0147735 | 1.458899e-01 | 1.387679 | 1.495226 | 1.385856 | 1.430908 |
| USDJPY | apARCH | 0.2048678 | 77 | 0.0985749 | 9.178584e+04 | -68.100393 | -67.973747 | -68.102883 | -68.049491 |
| USDJPY | iGARCH | 0.0124708 | 540 | 0.0147686 | 1.353186e-01 | 1.396558 | 1.476821 | 1.395498 | 1.428820 |
| USDJPY | csGARCH | 0.0124440 | 540 | 0.0147687 | 1.316635e-01 | 1.403047 | 1.524237 | 1.400764 | 1.451759 |
6.3.1.1 : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 0.0018221 | 3780 | 0.0021154 | 11.41958 | -6.528979 | -6.442381 | -6.530181 | -6.494171 |
| fGARCH.GARCH | 0.0018811 | 3780 | 0.0021154 | 11.42009 | -6.528962 | -6.442364 | -6.530164 | -6.494153 |
| fGARCH.TGARCH | 0.0013419 | 3780 | 0.0021157 | 11.60582 | -6.334633 | -6.234387 | -6.336215 | -6.294338 |
| fGARCH.AVGARCH | 0.0063876 | 221 | 0.0361413 | 75.00683 | -5.610021 | -5.500452 | -5.611894 | -5.565980 |
| fGARCH.NGARCH | 0.0304150 | 3780 | 0.0021003 | 4573.73568 | -14.952539 | -14.852293 | -14.954121 | -14.912244 |
| fGARCH.NAGARCH | 0.0014274 | 3780 | 0.0021156 | 52.78571 | -6.308381 | -6.208136 | -6.309964 | -6.268087 |
| fGARCH.APARCH | 33.3437862 | 1210 | -0.0485021 | 5745.21391 | -17.180876 | -17.068329 | -17.182839 | -17.135636 |
| fGARCH.GJRGARCH | 0.0015669 | 3780 | 0.0021156 | 11.41909 | -6.536140 | -6.435894 | -6.537722 | -6.495845 |
| fGARCH.ALLGARCH | 0.0409243 | 1413 | 0.0056038 | 2722.81125 | -11.224041 | -11.097706 | -11.226494 | -11.173259 |
| eGARCH | 0.0034735 | 2549 | 0.0031358 | 13.66246 | -6.597301 | -6.497771 | -6.598863 | -6.557293 |
| gjrGARCH | 0.0015995 | 3780 | 0.0021156 | 11.43985 | -6.549913 | -6.449668 | -6.551496 | -6.509619 |
| apARCH | 0.0290541 | 543 | 0.0146260 | 13455.05333 | -16.557354 | -16.445977 | -16.559281 | -16.512586 |
| iGARCH | 0.0017908 | 3780 | 0.0021155 | 11.41345 | -6.524279 | -6.451329 | -6.525154 | -6.494956 |
| csGARCH | 0.0017871 | 3780 | 0.0021155 | 11.39974 | -6.519492 | -6.405598 | -6.521508 | -6.473712 |
6.3.1.2 : Table summary
| Model | n |
|---|---|
| fGARCH.GARCH | 2 |
| fGARCH.NGARCH | 13 |
| fGARCH.APARCH | 5 |
| fGARCH.ALLGARCH | 2 |
| eGARCH | 4 |
| apARCH | 5 |
6.3.1.3 : Table summary
## selected models' filtered highest price.
hp <- united.fx2 %>%
separate(Type, c('Cur', 'Type')) %>%
dplyr::filter(Type == 'Hi') %>% dplyr::select(-Cur, -Type)
acc <- hp %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 3.000000e-07 | 559 | 1.431130e-02 | 1.521648e-01 | -7.437208 | -7.359273 | -7.438181 | -7.405881 |
| USDAUD | fGARCH.GARCH | 3.000000e-07 | 559 | 1.431130e-02 | 1.520092e-01 | -7.437344 | -7.359409 | -7.438317 | -7.406017 |
| USDAUD | fGARCH.TGARCH | 3.500000e-06 | 559 | 1.431130e-02 | 7.058772e-01 | -7.144229 | -7.052640 | -7.145549 | -7.107414 |
| USDAUD | fGARCH.NGARCH | 1.106692e+66 | 559 | -3.959543e+63 | 2.030200e+03 | -9.202063 | -9.110475 | -9.203383 | -9.165248 |
| USDAUD | fGARCH.NAGARCH | 3.000000e-07 | 559 | 1.431130e-02 | 1.580276e-01 | -7.450223 | -7.358635 | -7.451544 | -7.413408 |
| USDAUD | fGARCH.GJRGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 1.561037e-01 | -7.437738 | -7.346149 | -7.439058 | -7.400923 |
| USDAUD | gjrGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 1.584622e-01 | -7.444678 | -7.353089 | -7.445998 | -7.407863 |
| USDAUD | iGARCH | 3.000000e-07 | 559 | 1.431130e-02 | 1.523136e-01 | -7.439802 | -7.375520 | -7.440482 | -7.413963 |
| USDAUD | csGARCH | 3.000000e-07 | 559 | 1.431130e-02 | 1.514441e-01 | -7.422979 | -7.317737 | -7.424699 | -7.380676 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 8.000000e-07 | 559 | 1.431130e-02 | 2.720759e-01 | -8.490468 | -8.407383 | -8.491564 | -8.457071 |
| USDEUR | fGARCH.GARCH | 8.000000e-07 | 559 | 1.431130e-02 | 2.705361e-01 | -8.490991 | -8.407906 | -8.492087 | -8.457594 |
| USDEUR | fGARCH.TGARCH | 1.800000e-06 | 559 | 1.431130e-02 | 3.522086e-01 | -8.344873 | -8.248135 | -8.346336 | -8.305988 |
| USDEUR | fGARCH.NGARCH | 1.300000e-06 | 559 | 1.431130e-02 | 7.045336e+03 | -20.671898 | -20.575160 | -20.673361 | -20.633013 |
| USDEUR | fGARCH.NAGARCH | 7.000000e-07 | 559 | 1.431130e-02 | 2.721233e-01 | -8.490133 | -8.393395 | -8.491597 | -8.451248 |
| USDEUR | fGARCH.GJRGARCH | 7.000000e-07 | 559 | 1.431130e-02 | 2.684809e-01 | -8.490216 | -8.393478 | -8.491679 | -8.451331 |
| USDEUR | gjrGARCH | 7.000000e-07 | 559 | 1.431130e-02 | 2.573258e-01 | -8.512878 | -8.416141 | -8.514342 | -8.473994 |
| USDEUR | iGARCH | 8.000000e-07 | 559 | 1.431130e-02 | 2.649865e-01 | -8.489482 | -8.420051 | -8.490265 | -8.461574 |
| USDEUR | csGARCH | 7.000000e-07 | 559 | 1.431130e-02 | 2.273320e-01 | -8.491418 | -8.381027 | -8.493301 | -8.447045 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 1.255523e-01 | -9.101342 | -9.017778 | -9.102477 | -9.067754 |
| USDGBP | fGARCH.GARCH | 1.000000e-07 | 559 | 1.431130e-02 | 1.254537e-01 | -9.101389 | -9.017825 | -9.102524 | -9.067801 |
| USDGBP | fGARCH.TGARCH | 4.000000e-07 | 559 | 1.431130e-02 | 7.100763e-01 | -8.786098 | -8.688894 | -8.787601 | -8.747027 |
| USDGBP | fGARCH.NGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 1.125841e+03 | -9.681669 | -9.584464 | -9.683171 | -9.642598 |
| USDGBP | fGARCH.NAGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 1.435870e+02 | -8.426095 | -8.328891 | -8.427597 | -8.387024 |
| USDGBP | fGARCH.GJRGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 1.267718e-01 | -9.111770 | -9.014566 | -9.113273 | -9.072699 |
| USDGBP | gjrGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 1.063133e-01 | -9.127723 | -9.030519 | -9.129226 | -9.088652 |
| USDGBP | iGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 1.262008e-01 | -9.100764 | -9.030840 | -9.101584 | -9.072659 |
| USDGBP | csGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 7.665450e-02 | -9.099947 | -8.989103 | -9.101870 | -9.055394 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 3.100000e-06 | 559 | 1.431130e-02 | 4.377709e-01 | -7.669915 | -7.587337 | -7.670999 | -7.636721 |
| USDCHF | fGARCH.GARCH | 3.100000e-06 | 559 | 1.431130e-02 | 4.375650e-01 | -7.669689 | -7.587111 | -7.670773 | -7.636495 |
| USDCHF | fGARCH.TGARCH | 5.000000e-07 | 559 | 1.431130e-02 | 2.843040e-01 | -7.707818 | -7.611585 | -7.709267 | -7.669136 |
| USDCHF | fGARCH.NGARCH | 7.073077e-01 | 559 | 1.178070e-02 | 2.646208e+03 | -12.110031 | -12.013799 | -12.111481 | -12.071349 |
| USDCHF | fGARCH.NAGARCH | 1.500000e-06 | 559 | 1.431130e-02 | 1.414517e+02 | -6.794313 | -6.698080 | -6.795762 | -6.755630 |
| USDCHF | fGARCH.GJRGARCH | 2.000000e-06 | 559 | 1.431130e-02 | 4.085573e-01 | -7.694735 | -7.598502 | -7.696185 | -7.656053 |
| USDCHF | gjrGARCH | 1.900000e-06 | 559 | 1.431130e-02 | 4.185573e-01 | -7.719767 | -7.623534 | -7.721216 | -7.681084 |
| USDCHF | iGARCH | 3.100000e-06 | 559 | 1.431130e-02 | 4.793057e-01 | -7.647093 | -7.578172 | -7.647865 | -7.619389 |
| USDCHF | csGARCH | 3.100000e-06 | 559 | 1.431130e-02 | 4.419797e-01 | -7.646381 | -7.536492 | -7.648248 | -7.602209 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 9.000000e-07 | 559 | 1.431130e-02 | 1.544139e-01 | -8.170387 | -8.080613 | -8.171666 | -8.134301 |
| USDCAD | fGARCH.GARCH | 9.000000e-07 | 559 | 1.431130e-02 | 1.545209e-01 | -8.170531 | -8.080757 | -8.171810 | -8.134445 |
| USDCAD | fGARCH.TGARCH | 2.000000e-06 | 559 | 1.431130e-02 | 9.016971e-01 | -7.931385 | -7.827958 | -7.933057 | -7.889811 |
| USDCAD | fGARCH.NGARCH | 3.065824e+120 | 559 | -1.096896e+118 | 1.621092e+04 | -45.241236 | -45.137808 | -45.242908 | -45.199662 |
| USDCAD | fGARCH.NAGARCH | 7.000000e-07 | 559 | 1.431130e-02 | 1.531831e-01 | -8.177455 | -8.074028 | -8.179127 | -8.135881 |
| USDCAD | fGARCH.GJRGARCH | 8.000000e-07 | 559 | 1.431130e-02 | 1.498210e-01 | -8.169686 | -8.066259 | -8.171359 | -8.128113 |
| USDCAD | gjrGARCH | 7.000000e-07 | 559 | 1.431130e-02 | 1.471574e-01 | -8.172520 | -8.069093 | -8.174192 | -8.130946 |
| USDCAD | iGARCH | 9.000000e-07 | 559 | 1.431130e-02 | 1.547462e-01 | -8.171812 | -8.095691 | -8.172751 | -8.141214 |
| USDCAD | csGARCH | 1.000000e-06 | 559 | 1.431130e-02 | 1.532442e-01 | -8.153903 | -8.036823 | -8.156021 | -8.106841 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 6.300000e-05 | 559 | 1.431100e-02 | 4.477761e-01 | -6.249283 | -6.153511 | -6.250731 | -6.210787 |
| USDCNY | fGARCH.GARCH | 6.280000e-05 | 559 | 1.431100e-02 | 4.492890e-01 | -6.248594 | -6.152823 | -6.250043 | -6.210099 |
| USDCNY | fGARCH.TGARCH | 3.970000e-05 | 559 | 1.431110e-02 | 2.481502e+00 | -5.892319 | -5.782905 | -5.894183 | -5.848340 |
| USDCNY | fGARCH.NGARCH | 6.540000e-05 | 559 | 1.431100e-02 | 6.115255e+02 | -7.306839 | -7.197425 | -7.308702 | -7.262860 |
| USDCNY | fGARCH.NAGARCH | 3.950000e-05 | 559 | 1.431110e-02 | 4.102266e-01 | -6.279606 | -6.170192 | -6.281470 | -6.235627 |
| USDCNY | fGARCH.GJRGARCH | 4.260000e-05 | 559 | 1.431110e-02 | 4.361674e-01 | -6.260008 | -6.150595 | -6.261872 | -6.216030 |
| USDCNY | gjrGARCH | 3.630000e-05 | 559 | 1.431110e-02 | 4.557971e-01 | -6.274817 | -6.165403 | -6.276680 | -6.230838 |
| USDCNY | iGARCH | 6.260000e-05 | 559 | 1.431100e-02 | 4.394265e-01 | -6.235814 | -6.153685 | -6.236899 | -6.202802 |
| USDCNY | csGARCH | 6.190000e-05 | 559 | 1.431100e-02 | 4.574758e-01 | -6.240600 | -6.117543 | -6.242931 | -6.191137 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 1.377350e-02 | 559 | 1.426200e-02 | 1.333411e-01 | 1.400651 | 1.495488 | 1.399205 | 1.438771 |
| USDJPY | fGARCH.GARCH | 1.457990e-02 | 559 | 1.425910e-02 | 1.331475e-01 | 1.400950 | 1.495788 | 1.399504 | 1.439070 |
| USDJPY | fGARCH.TGARCH | 1.004660e-02 | 559 | 1.427530e-02 | 1.775850e-01 | 1.428467 | 1.536947 | 1.426610 | 1.472071 |
| USDJPY | fGARCH.NGARCH | 2.972860e+246 | 559 | -1.063635e+244 | 5.051013e+03 | -3.692083 | -3.583603 | -3.693940 | -3.648479 |
| USDJPY | fGARCH.NAGARCH | 1.162970e-02 | 559 | 1.426970e-02 | 1.387974e-01 | 1.389546 | 1.498027 | 1.387689 | 1.433150 |
| USDJPY | fGARCH.GJRGARCH | 1.193290e-02 | 559 | 1.426860e-02 | 1.353829e-01 | 1.396830 | 1.505310 | 1.394973 | 1.440433 |
| USDJPY | gjrGARCH | 1.278950e-02 | 559 | 1.426550e-02 | 1.449849e-01 | 1.390041 | 1.498521 | 1.388184 | 1.433644 |
| USDJPY | iGARCH | 1.454770e-02 | 559 | 1.425920e-02 | 1.344519e-01 | 1.398596 | 1.479791 | 1.397509 | 1.431232 |
| USDJPY | csGARCH | 1.292400e-02 | 559 | 1.426500e-02 | 1.309096e-01 | 1.405506 | 1.527629 | 1.403186 | 1.454594 |
6.3.2.1A : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 1.977400e-03 | 3913 | 2.043500e-03 | 11.42366 | -6.531136 | -6.444344 | -6.532345 | -6.496249 |
| fGARCH.GARCH | 2.092600e-03 | 3913 | 2.043400e-03 | 11.42467 | -6.531084 | -6.444292 | -6.532293 | -6.496198 |
| fGARCH.TGARCH | 1.442100e-03 | 3913 | 2.043700e-03 | 11.60227 | -6.339751 | -6.239310 | -6.341341 | -6.299378 |
| fGARCH.NGARCH | 4.246942e+245 | 3913 | -2.170684e+242 | 5131.97873 | -15.415117 | -15.314676 | -15.416707 | -15.374744 |
| fGARCH.NAGARCH | 1.667500e-03 | 3913 | 2.043600e-03 | 51.38677 | -6.318326 | -6.217885 | -6.319915 | -6.277953 |
| fGARCH.GJRGARCH | 1.711300e-03 | 3913 | 2.043600e-03 | 11.42364 | -6.538189 | -6.437748 | -6.539779 | -6.497816 |
| gjrGARCH | 1.832800e-03 | 3913 | 2.043500e-03 | 11.44392 | -6.551763 | -6.451322 | -6.553353 | -6.511390 |
| iGARCH | 2.087900e-03 | 3913 | 2.043400e-03 | 11.41716 | -6.526596 | -6.453453 | -6.527477 | -6.497196 |
| csGARCH | 1.855900e-03 | 3913 | 2.043500e-03 | 11.40387 | -6.521389 | -6.407299 | -6.523412 | -6.475530 |
6.3.2.1B : Table summary
| Model | n |
|---|---|
| fGARCH.NGARCH | 8 |
6.3.2.1C : Table summary
## selected models' filtered highest price.
hp <- united.fx3 %>%
separate(Type, c('Cur', 'Type')) %>%
dplyr::filter(Type == 'Hi') %>% dplyr::select(-Cur, -Type)
acc <- hp %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 0.0000003 | 488 | 0.0163934 | 1.602351e-01 | -7.413920 | -7.336564 | -7.414875 | -7.382826 |
| USDAUD | fGARCH.GARCH | 0.0000004 | 488 | 0.0163934 | 1.600933e-01 | -7.414158 | -7.336802 | -7.415113 | -7.383064 |
| USDAUD | fGARCH.TGARCH | 0.0000040 | 488 | 0.0163934 | 7.691443e-01 | -7.093541 | -7.002531 | -7.094840 | -7.056958 |
| USDAUD | fGARCH.NGARCH | 0.0000034 | 488 | 0.0163934 | 1.818437e+03 | -8.541492 | -8.450482 | -8.542791 | -8.504909 |
| USDAUD | fGARCH.NAGARCH | 0.0000003 | 488 | 0.0163934 | 1.664752e-01 | -7.426789 | -7.335780 | -7.428089 | -7.390207 |
| USDAUD | fGARCH.GJRGARCH | 0.0000002 | 488 | 0.0163934 | 1.645588e-01 | -7.414576 | -7.323566 | -7.415875 | -7.377993 |
| USDAUD | gjrGARCH | 0.0000002 | 488 | 0.0163934 | 1.671197e-01 | -7.421436 | -7.330427 | -7.422736 | -7.384854 |
| USDAUD | iGARCH | 0.0000003 | 488 | 0.0163934 | 1.604301e-01 | -7.416498 | -7.352795 | -7.417162 | -7.390892 |
| USDAUD | csGARCH | 0.0000003 | 488 | 0.0163934 | 1.595026e-01 | -7.399932 | -7.295269 | -7.401629 | -7.357861 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 0.0000008 | 488 | 0.0163934 | 2.620646e-01 | -8.433867 | -8.351312 | -8.434947 | -8.400683 |
| USDEUR | fGARCH.GARCH | 0.0000008 | 488 | 0.0163934 | 2.604992e-01 | -8.434583 | -8.352028 | -8.435663 | -8.401399 |
| USDEUR | fGARCH.TGARCH | 0.0000020 | 488 | 0.0163934 | 3.427126e-01 | -8.283036 | -8.186828 | -8.284481 | -8.244364 |
| USDEUR | fGARCH.NGARCH | 0.0000012 | 488 | 0.0163934 | 6.424638e+03 | -19.605219 | -19.509010 | -19.606664 | -19.566547 |
| USDEUR | fGARCH.NAGARCH | 0.0000007 | 488 | 0.0163934 | 2.614256e-01 | -8.433155 | -8.336947 | -8.434600 | -8.394483 |
| USDEUR | fGARCH.GJRGARCH | 0.0000007 | 488 | 0.0163934 | 2.575236e-01 | -8.433385 | -8.337176 | -8.434830 | -8.394713 |
| USDEUR | gjrGARCH | 0.0000007 | 488 | 0.0163934 | 2.467177e-01 | -8.457801 | -8.361592 | -8.459246 | -8.419129 |
| USDEUR | iGARCH | 0.0000007 | 488 | 0.0163934 | 2.546220e-01 | -8.433181 | -8.364280 | -8.433950 | -8.405486 |
| USDEUR | csGARCH | 0.0000007 | 488 | 0.0163934 | 2.151788e-01 | -8.438091 | -8.328229 | -8.439954 | -8.393931 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 0.0000001 | 488 | 0.0163934 | 1.224075e-01 | -9.060843 | -8.977762 | -9.061961 | -9.027449 |
| USDGBP | fGARCH.GARCH | 0.0000001 | 488 | 0.0163934 | 1.222611e-01 | -9.060867 | -8.977786 | -9.061985 | -9.027473 |
| USDGBP | fGARCH.TGARCH | 0.0000004 | 488 | 0.0163934 | 6.847148e-01 | -8.741755 | -8.645035 | -8.743238 | -8.702879 |
| USDGBP | fGARCH.NGARCH | 0.0000003 | 488 | 0.0163934 | 1.288644e+03 | -9.777068 | -9.680348 | -9.778551 | -9.738192 |
| USDGBP | fGARCH.NAGARCH | 0.0000001 | 488 | 0.0163934 | 3.623999e+01 | -8.801648 | -8.704928 | -8.803132 | -8.762772 |
| USDGBP | fGARCH.GJRGARCH | 0.0000001 | 488 | 0.0163934 | 1.239584e-01 | -9.071650 | -8.974930 | -9.073134 | -9.032774 |
| USDGBP | gjrGARCH | 0.0000001 | 488 | 0.0163934 | 1.013262e-01 | -9.088965 | -8.992245 | -9.090449 | -9.050089 |
| USDGBP | iGARCH | 0.0000001 | 488 | 0.0163934 | 1.232742e-01 | -9.060361 | -8.990918 | -9.061166 | -9.032449 |
| USDGBP | csGARCH | 0.0000001 | 488 | 0.0163934 | 6.849260e-02 | -9.062573 | -8.952215 | -9.064476 | -9.018216 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 0.0000034 | 488 | 0.0163934 | 4.109802e-01 | -7.630888 | -7.547264 | -7.631999 | -7.597274 |
| USDCHF | fGARCH.GARCH | 0.0000034 | 488 | 0.0163934 | 4.108674e-01 | -7.630712 | -7.547088 | -7.631824 | -7.597098 |
| USDCHF | fGARCH.TGARCH | 0.0000005 | 488 | 0.0163934 | 2.773429e-01 | -7.672479 | -7.575199 | -7.673960 | -7.633376 |
| USDCHF | fGARCH.NGARCH | 0.0000032 | 488 | 0.0163934 | 2.352317e+03 | -11.695242 | -11.597962 | -11.696723 | -11.656139 |
| USDCHF | fGARCH.NAGARCH | 0.0000016 | 488 | 0.0163934 | 1.617116e+02 | -6.607460 | -6.510180 | -6.608941 | -6.568357 |
| USDCHF | fGARCH.GJRGARCH | 0.0000021 | 488 | 0.0163934 | 3.868017e-01 | -7.655018 | -7.557738 | -7.656498 | -7.615914 |
| USDCHF | gjrGARCH | 0.0000021 | 488 | 0.0163934 | 4.049463e-01 | -7.675492 | -7.578213 | -7.676973 | -7.636389 |
| USDCHF | iGARCH | 0.0000034 | 488 | 0.0163934 | 4.536987e-01 | -7.607004 | -7.537036 | -7.607800 | -7.578879 |
| USDCHF | csGARCH | 0.0000035 | 488 | 0.0163934 | 4.158965e-01 | -7.607232 | -7.496296 | -7.609134 | -7.562639 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 0.0000009 | 488 | 0.0163934 | 1.592022e-01 | -8.145785 | -8.056350 | -8.147056 | -8.109836 |
| USDCAD | fGARCH.GARCH | 0.0000009 | 488 | 0.0163934 | 1.593247e-01 | -8.145870 | -8.056435 | -8.147141 | -8.109920 |
| USDCAD | fGARCH.TGARCH | 0.0000020 | 488 | 0.0163934 | 9.657899e-01 | -7.881463 | -7.778375 | -7.883127 | -7.840026 |
| USDCAD | fGARCH.NGARCH | 0.0000287 | 488 | 0.0163933 | 1.705915e+04 | -47.046763 | -46.943675 | -47.048426 | -47.005326 |
| USDCAD | fGARCH.NAGARCH | 0.0000007 | 488 | 0.0163934 | 1.572375e-01 | -8.151830 | -8.048742 | -8.153493 | -8.110393 |
| USDCAD | fGARCH.GJRGARCH | 0.0000007 | 488 | 0.0163934 | 1.543806e-01 | -8.145249 | -8.042161 | -8.146912 | -8.103812 |
| USDCAD | gjrGARCH | 0.0000007 | 488 | 0.0163934 | 1.514822e-01 | -8.148257 | -8.045169 | -8.149920 | -8.106819 |
| USDCAD | iGARCH | 0.0000009 | 488 | 0.0163934 | 1.600594e-01 | -8.147144 | -8.071362 | -8.148077 | -8.116682 |
| USDCAD | csGARCH | 0.0000008 | 488 | 0.0163934 | 1.578783e-01 | -8.128842 | -8.012100 | -8.130949 | -8.081916 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 0.0000704 | 488 | 0.0163932 | 4.611488e-01 | -6.279142 | -6.181995 | -6.280631 | -6.240094 |
| USDCNY | fGARCH.GARCH | 0.0000702 | 488 | 0.0163932 | 4.629284e-01 | -6.278352 | -6.181205 | -6.279841 | -6.239304 |
| USDCNY | fGARCH.TGARCH | 0.0000424 | 488 | 0.0163933 | 2.722591e+00 | -5.923592 | -5.812803 | -5.925501 | -5.879060 |
| USDCNY | fGARCH.NGARCH | 0.0000729 | 488 | 0.0163931 | 7.001926e+02 | -7.488744 | -7.377956 | -7.490654 | -7.444213 |
| USDCNY | fGARCH.NAGARCH | 0.0000447 | 488 | 0.0163933 | 4.172108e-01 | -6.311264 | -6.200475 | -6.313173 | -6.266732 |
| USDCNY | fGARCH.GJRGARCH | 0.0000477 | 488 | 0.0163932 | 4.484135e-01 | -6.289018 | -6.178229 | -6.290927 | -6.244487 |
| USDCNY | gjrGARCH | 0.0000408 | 488 | 0.0163933 | 4.680574e-01 | -6.305894 | -6.195106 | -6.307804 | -6.261363 |
| USDCNY | iGARCH | 0.0000699 | 488 | 0.0163932 | 4.524095e-01 | -6.265234 | -6.181729 | -6.266355 | -6.231669 |
| USDCNY | csGARCH | 0.0000692 | 488 | 0.0163932 | 4.723495e-01 | -6.269365 | -6.144935 | -6.271748 | -6.219351 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 0.0144486 | 488 | 0.0163342 | 1.236987e-01 | 1.442813 | 1.538416 | 1.441347 | 1.481240 |
| USDJPY | fGARCH.GARCH | 0.0149123 | 488 | 0.0163323 | 1.236375e-01 | 1.442851 | 1.538454 | 1.441385 | 1.481278 |
| USDJPY | fGARCH.TGARCH | 0.0107038 | 488 | 0.0163496 | 1.720809e-01 | 1.473414 | 1.582659 | 1.471534 | 1.517325 |
| USDJPY | fGARCH.NGARCH | 0.2239441 | 488 | 0.0154756 | 2.440676e+03 | -3.136883 | -3.027639 | -3.138764 | -3.092973 |
| USDJPY | fGARCH.NAGARCH | 0.0118146 | 488 | 0.0163450 | 1.280069e-01 | 1.432188 | 1.541433 | 1.430308 | 1.476099 |
| USDJPY | fGARCH.GJRGARCH | 0.0118311 | 488 | 0.0163450 | 1.249952e-01 | 1.439273 | 1.548518 | 1.437393 | 1.483184 |
| USDJPY | gjrGARCH | 0.0130039 | 488 | 0.0163401 | 1.347595e-01 | 1.432997 | 1.542242 | 1.431116 | 1.476908 |
| USDJPY | iGARCH | 0.0152216 | 488 | 0.0163311 | 1.246938e-01 | 1.440992 | 1.522954 | 1.439888 | 1.473937 |
| USDJPY | csGARCH | 0.0141645 | 488 | 0.0163354 | 1.216824e-01 | 1.447162 | 1.570048 | 1.444815 | 1.496556 |
6.3.2.2A : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 0.0020749 | 3416 | 0.0023407 | 11.42246 | -6.503090 | -6.416119 | -6.504303 | -6.468132 |
| fGARCH.GARCH | 0.0021411 | 3416 | 0.0023407 | 11.42304 | -6.503099 | -6.416127 | -6.504312 | -6.468140 |
| fGARCH.TGARCH | 0.0015364 | 3416 | 0.0023410 | 11.63014 | -6.303207 | -6.202587 | -6.304802 | -6.262763 |
| fGARCH.NGARCH | 0.0320077 | 3416 | 0.0023232 | 4772.65257 | -15.327344 | -15.226725 | -15.328939 | -15.286900 |
| fGARCH.NAGARCH | 0.0016947 | 3416 | 0.0023409 | 39.20931 | -6.328565 | -6.227946 | -6.330160 | -6.288121 |
| fGARCH.GJRGARCH | 0.0016975 | 3416 | 0.0023409 | 11.42360 | -6.509946 | -6.409326 | -6.511541 | -6.469501 |
| gjrGARCH | 0.0018641 | 3416 | 0.0023408 | 11.44628 | -6.523550 | -6.422930 | -6.525144 | -6.483105 |
| iGARCH | 0.0021853 | 3416 | 0.0023406 | 11.41640 | -6.498347 | -6.425024 | -6.499231 | -6.468874 |
| csGARCH | 0.0020342 | 3416 | 0.0023407 | 11.40475 | -6.494125 | -6.379857 | -6.496154 | -6.448194 |
6.3.2.2B : Table summary
| Model | n |
|---|---|
6.3.2.2C : Table summary
## filtered bias lowest price.
lp <- fx %>% separate(Type, c('Cur', 'Type')) %>%
dplyr::filter(Type == 'Lo') %>%
dplyr::select(-Cur, -Type)
ntmID <- lp %>% dplyr::filter(se == 1) %>% .$Date %>% unlist %>% sort
acc <- lp %>% dplyr::filter(!Date %in% ntmID & Date %in% ntimeID2) %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 0.0000003 | 501 | 0.0159681 | 1.698809e-01 | -7.4479972 | -7.369647 | -7.4489688 | -7.416503 |
| USDAUD | fGARCH.GARCH | 0.0000003 | 501 | 0.0159681 | 1.699739e-01 | -7.4479377 | -7.369588 | -7.4489093 | -7.416444 |
| USDAUD | fGARCH.TGARCH | 0.0000024 | 501 | 0.0159681 | 8.852862e-01 | -7.1571966 | -7.065193 | -7.1585170 | -7.120215 |
| USDAUD | fGARCH.AVGARCH | 0.0000000 | 50 | 0.1600000 | 1.954909e+02 | -5.7686745 | -5.667345 | -5.7702560 | -5.727944 |
| USDAUD | fGARCH.NGARCH | 0.0000061 | 501 | 0.0159680 | 1.537787e+04 | -41.1917707 | -41.099767 | -41.1930911 | -41.154789 |
| USDAUD | fGARCH.NAGARCH | 0.0000006 | 501 | 0.0159681 | 1.945351e-01 | -7.4472857 | -7.355282 | -7.4486061 | -7.410304 |
| USDAUD | fGARCH.APARCH | 0.0000043 | 214 | 0.0373831 | 7.340472e+03 | -21.6955859 | -21.588280 | -21.6973543 | -21.652451 |
| USDAUD | fGARCH.GJRGARCH | 0.0000013 | 501 | 0.0159681 | 1.924704e-01 | -7.4414192 | -7.349416 | -7.4427396 | -7.404437 |
| USDAUD | fGARCH.ALLGARCH | 0.0000005 | 116 | 0.0689655 | 5.849167e+03 | -17.9617198 | -17.839361 | -17.9640148 | -17.912535 |
| USDAUD | eGARCH | 0.0000005 | 329 | 0.0243161 | 1.083287e+01 | -7.4813576 | -7.386725 | -7.4827525 | -7.443318 |
| USDAUD | gjrGARCH | 0.0000013 | 501 | 0.0159681 | 1.934094e-01 | -7.4466578 | -7.354654 | -7.4479782 | -7.409676 |
| USDAUD | apARCH | 0.0000001 | 77 | 0.1038961 | 3.436000e-03 | -7.9376104 | -7.831359 | -7.9393650 | -7.894900 |
| USDAUD | iGARCH | 0.0000013 | 501 | 0.0159681 | 1.881442e-01 | -7.4452882 | -7.380591 | -7.4459648 | -7.419282 |
| USDAUD | csGARCH | 0.0000007 | 501 | 0.0159681 | 1.891122e-01 | -7.4270989 | -7.321442 | -7.4288212 | -7.384629 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 0.0000002 | 501 | 0.0159681 | 2.858257e-01 | -8.4204421 | -8.339431 | -8.4215016 | -8.387879 |
| USDEUR | fGARCH.GARCH | 0.0000002 | 501 | 0.0159681 | 2.862249e-01 | -8.4202747 | -8.339263 | -8.4213341 | -8.387711 |
| USDEUR | fGARCH.TGARCH | 0.0000007 | 501 | 0.0159681 | 5.415538e-01 | -8.2192615 | -8.124597 | -8.2206798 | -8.181210 |
| USDEUR | fGARCH.AVGARCH | 0.0000000 | 26 | 0.3076923 | 4.485169e-01 | -7.8175320 | -7.716716 | -7.8190856 | -7.777008 |
| USDEUR | fGARCH.NGARCH | 0.0000068 | 501 | 0.0159680 | 1.423859e+04 | -32.4008824 | -32.306218 | -32.4023006 | -32.362831 |
| USDEUR | fGARCH.NAGARCH | 0.0000002 | 501 | 0.0159681 | 1.356104e+02 | -7.9105714 | -7.815907 | -7.9119896 | -7.872520 |
| USDEUR | fGARCH.APARCH | 0.0000000 | 87 | 0.0919540 | 2.891776e+03 | -13.8058686 | -13.703357 | -13.8074978 | -13.764662 |
| USDEUR | fGARCH.GJRGARCH | 0.0000002 | 501 | 0.0159681 | 2.864656e-01 | -8.4256324 | -8.330968 | -8.4270507 | -8.387581 |
| USDEUR | fGARCH.ALLGARCH | 0.0000000 | 227 | 0.0352423 | 2.277380e-02 | -8.4434249 | -8.324501 | -8.4456099 | -8.395620 |
| USDEUR | eGARCH | 0.0000001 | 331 | 0.0241692 | 2.605695e+00 | -8.5833882 | -8.489002 | -8.5848077 | -8.545448 |
| USDEUR | gjrGARCH | 0.0000002 | 501 | 0.0159681 | 2.903109e-01 | -8.4421315 | -8.347467 | -8.4435497 | -8.404080 |
| USDEUR | apARCH | 0.0000000 | 77 | 0.1038961 | 3.782000e-04 | -8.3199640 | -8.217803 | -8.3215816 | -8.278899 |
| USDEUR | iGARCH | 0.0000002 | 501 | 0.0159681 | 2.822404e-01 | -8.4176028 | -8.350245 | -8.4183570 | -8.390527 |
| USDEUR | csGARCH | 0.0000002 | 501 | 0.0159681 | 2.802158e-01 | -8.3994318 | -8.291114 | -8.4012618 | -8.355892 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 0.0000000 | 501 | 0.0159681 | 7.817640e-02 | -9.1208010 | -9.043758 | -9.1217555 | -9.089834 |
| USDGBP | fGARCH.GARCH | 0.0000002 | 501 | 0.0159681 | 7.986670e-02 | -9.1179617 | -9.040919 | -9.1189162 | -9.086995 |
| USDGBP | fGARCH.TGARCH | 0.0000001 | 501 | 0.0159681 | 2.505006e-01 | -8.8978017 | -8.807120 | -8.8990990 | -8.861353 |
| USDGBP | fGARCH.AVGARCH | 0.0000001 | 31 | 0.2580645 | 1.239286e-01 | -9.0826534 | -8.972345 | -9.0845693 | -9.038317 |
| USDGBP | fGARCH.NGARCH | 0.0000024 | 501 | 0.0159681 | 1.130324e+03 | -11.0869884 | -10.996307 | -11.0882857 | -11.050539 |
| USDGBP | fGARCH.NAGARCH | 0.0000000 | 501 | 0.0159681 | 2.180841e+01 | -8.9166835 | -8.826002 | -8.9179809 | -8.880235 |
| USDGBP | fGARCH.APARCH | 0.0000001 | 214 | 0.0373832 | 2.913752e+00 | -8.6845140 | -8.582964 | -8.6861056 | -8.643696 |
| USDGBP | fGARCH.GJRGARCH | 0.0000000 | 501 | 0.0159681 | 8.164340e-02 | -9.1333936 | -9.042712 | -9.1346909 | -9.096945 |
| USDGBP | fGARCH.ALLGARCH | 0.0000000 | 228 | 0.0350877 | 7.542930e-02 | -9.0719695 | -8.956418 | -9.0740130 | -9.025524 |
| USDGBP | eGARCH | 0.0000001 | 329 | 0.0243161 | 1.337176e-01 | -9.1959246 | -9.102902 | -9.1973001 | -9.158534 |
| USDGBP | gjrGARCH | 0.0000000 | 501 | 0.0159681 | 8.378780e-02 | -9.1433216 | -9.052640 | -9.1446189 | -9.106873 |
| USDGBP | apARCH | 0.0000000 | 77 | 0.1038961 | 2.715700e-03 | -9.2779020 | -9.171410 | -9.2796738 | -9.235100 |
| USDGBP | iGARCH | 0.0000002 | 501 | 0.0159681 | 8.141310e-02 | -9.1170166 | -9.053613 | -9.1176820 | -9.091532 |
| USDGBP | csGARCH | 0.0000001 | 501 | 0.0159681 | 7.809850e-02 | -9.0999361 | -8.995616 | -9.1016292 | -9.058005 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 0.0000087 | 501 | 0.0159680 | 3.619271e-01 | -7.7174082 | -7.637092 | -7.7184316 | -7.685124 |
| USDCHF | fGARCH.GARCH | 0.0000087 | 501 | 0.0159680 | 3.617428e-01 | -7.7172133 | -7.636897 | -7.7182366 | -7.684929 |
| USDCHF | fGARCH.TGARCH | 0.0000005 | 501 | 0.0159681 | 2.557967e-01 | -7.6581303 | -7.564158 | -7.6595101 | -7.620357 |
| USDCHF | fGARCH.AVGARCH | 0.0000002 | 16 | 0.5000000 | 9.931160e-02 | -7.8876405 | -7.784873 | -7.8892785 | -7.846326 |
| USDCHF | fGARCH.NGARCH | 0.0000071 | 501 | 0.0159680 | 8.505416e+02 | -9.0156812 | -8.921709 | -9.0170610 | -8.977908 |
| USDCHF | fGARCH.NAGARCH | 0.0000049 | 501 | 0.0159680 | 3.568887e-01 | -7.7419427 | -7.647971 | -7.7433225 | -7.704169 |
| USDCHF | fGARCH.APARCH | 0.0000000 | 213 | 0.0375587 | 7.681167e+03 | -25.4459808 | -25.348136 | -25.4474473 | -25.406648 |
| USDCHF | fGARCH.GJRGARCH | 0.0000052 | 501 | 0.0159680 | 3.123548e-01 | -7.7481130 | -7.654141 | -7.7494928 | -7.710340 |
| USDCHF | fGARCH.ALLGARCH | 0.0000000 | 226 | 0.0353982 | 3.610524e+02 | -9.1443610 | -9.032906 | -9.1462507 | -9.099557 |
| USDCHF | eGARCH | 0.0000001 | 329 | 0.0243161 | 1.454775e-01 | -8.0477821 | -7.958818 | -8.0490283 | -8.012021 |
| USDCHF | gjrGARCH | 0.0000067 | 501 | 0.0159680 | 3.166351e-01 | -7.7663807 | -7.672409 | -7.7677605 | -7.728607 |
| USDCHF | apARCH | 0.0000000 | 76 | 0.1052632 | 1.568400e-03 | -8.0253823 | -7.925513 | -8.0269191 | -7.985236 |
| USDCHF | iGARCH | 0.0003023 | 501 | 0.0159669 | 7.767458e-01 | -7.4807057 | -7.414045 | -7.4814263 | -7.453911 |
| USDCHF | csGARCH | 0.0000846 | 501 | 0.0159677 | 5.211560e-01 | -7.6154091 | -7.507781 | -7.6171984 | -7.572146 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 0.0000001 | 501 | 0.0159681 | 2.025376e-01 | -8.0659204 | -7.992072 | -8.0667794 | -8.036236 |
| USDCAD | fGARCH.GARCH | 0.0000002 | 501 | 0.0159681 | 2.026794e-01 | -8.0658538 | -7.992006 | -8.0667129 | -8.036170 |
| USDCAD | fGARCH.TGARCH | 0.0000010 | 501 | 0.0159681 | 6.189118e-01 | -7.8180690 | -7.730568 | -7.8192594 | -7.782897 |
| USDCAD | fGARCH.AVGARCH | 0.0000000 | 37 | 0.2162162 | 9.743570e-02 | -8.2867029 | -8.185956 | -8.2882652 | -8.246206 |
| USDCAD | fGARCH.NGARCH | 0.0000022 | 501 | 0.0159681 | 5.117681e+03 | -15.2790248 | -15.191524 | -15.2802151 | -15.243853 |
| USDCAD | fGARCH.NAGARCH | 0.0000001 | 501 | 0.0159681 | 2.030384e-01 | -8.0758249 | -7.988324 | -8.0770153 | -8.040653 |
| USDCAD | fGARCH.APARCH | 0.0000001 | 210 | 0.0380952 | 3.983092e+03 | -21.1158123 | -21.015120 | -21.1173746 | -21.075336 |
| USDCAD | fGARCH.GJRGARCH | 0.0000001 | 501 | 0.0159681 | 2.027792e-01 | -8.0669948 | -7.979494 | -8.0681851 | -8.031823 |
| USDCAD | fGARCH.ALLGARCH | 0.0000001 | 227 | 0.0352423 | 2.523510e+03 | -14.0754729 | -13.961308 | -14.0774635 | -14.029581 |
| USDCAD | eGARCH | 0.0000000 | 328 | 0.0243902 | 1.314520e+00 | -8.2697548 | -8.183910 | -8.2708975 | -8.235248 |
| USDCAD | gjrGARCH | 0.0000001 | 501 | 0.0159681 | 2.032634e-01 | -8.0736901 | -7.986189 | -8.0748804 | -8.038518 |
| USDCAD | apARCH | 0.0000000 | 76 | 0.1052632 | 1.973600e-03 | -8.4850007 | -8.382395 | -8.4866325 | -8.443756 |
| USDCAD | iGARCH | 0.0000004 | 501 | 0.0159681 | 2.029446e-01 | -8.0656830 | -8.005488 | -8.0662649 | -8.041487 |
| USDCAD | csGARCH | 0.0000002 | 501 | 0.0159681 | 2.013954e-01 | -8.0495033 | -7.948349 | -8.0510782 | -8.008843 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 0.0021891 | 501 | 0.0159593 | 2.779012e+00 | -6.3924320 | -6.306817 | -6.3935938 | -6.358019 |
| USDCNY | fGARCH.GARCH | 0.0012376 | 501 | 0.0159631 | 2.787831e+00 | -6.3907829 | -6.305168 | -6.3919448 | -6.356370 |
| USDCNY | fGARCH.TGARCH | 0.0039682 | 501 | 0.0159522 | 2.768388e+00 | -6.2929383 | -6.193682 | -6.2944766 | -6.253042 |
| USDCNY | fGARCH.AVGARCH | 0.0000002 | 12 | 0.6666666 | 1.992000e-03 | -7.0562794 | -6.947421 | -7.0580670 | -7.012529 |
| USDCNY | fGARCH.NGARCH | 0.0043008 | 501 | 0.0159509 | 6.882411e+02 | -7.5928785 | -7.493622 | -7.5944168 | -7.552982 |
| USDCNY | fGARCH.NAGARCH | 0.0007785 | 501 | 0.0159650 | 3.773821e+00 | -6.3396243 | -6.240368 | -6.3411626 | -6.299728 |
| USDCNY | fGARCH.APARCH | 0.0000093 | 211 | 0.0379146 | 4.651967e+03 | -15.5118885 | -15.396353 | -15.5139269 | -15.465449 |
| USDCNY | fGARCH.GJRGARCH | 0.0018019 | 501 | 0.0159609 | 3.380787e+00 | -6.3243521 | -6.225096 | -6.3258904 | -6.284456 |
| USDCNY | fGARCH.ALLGARCH | 0.0000014 | 227 | 0.0352423 | 1.788449e-01 | -7.5014423 | -7.370055 | -7.5040673 | -7.448631 |
| USDCNY | eGARCH | 0.0016127 | 327 | 0.0244550 | 4.432456e+00 | -6.4365728 | -6.334249 | -6.4382144 | -6.395443 |
| USDCNY | gjrGARCH | 0.0019140 | 501 | 0.0159604 | 2.784403e+00 | -6.4142318 | -6.314975 | -6.4157701 | -6.374336 |
| USDCNY | apARCH | 0.0000033 | 77 | 0.1038960 | 5.036400e-03 | -7.0149213 | -6.900121 | -7.0169322 | -6.968780 |
| USDCNY | iGARCH | 0.0023955 | 501 | 0.0159585 | 3.282410e+00 | -6.2632273 | -6.191254 | -6.2640660 | -6.234298 |
| USDCNY | csGARCH | 0.0024499 | 501 | 0.0159583 | 3.341171e+00 | -6.3026324 | -6.189734 | -6.3045997 | -6.257253 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 0.0123239 | 501 | 0.0159189 | 1.853500e-01 | 1.5552424 | 1.641094 | 1.5540522 | 1.589751 |
| USDJPY | fGARCH.GARCH | 0.0116739 | 501 | 0.0159215 | 1.850942e-01 | 1.5555134 | 1.641365 | 1.5543233 | 1.590021 |
| USDJPY | fGARCH.TGARCH | 0.0122742 | 501 | 0.0159191 | 2.616322e-01 | 1.5825867 | 1.682080 | 1.5810195 | 1.622578 |
| USDJPY | fGARCH.AVGARCH | 0.0615865 | 37 | 0.2128872 | 5.636226e-01 | 0.9338363 | 1.073338 | 0.9308645 | 0.989905 |
| USDJPY | fGARCH.NGARCH | 0.0175369 | 501 | 0.0158981 | 6.234807e+03 | -10.8934737 | -10.793980 | -10.8950408 | -10.853482 |
| USDJPY | fGARCH.NAGARCH | 0.0086337 | 501 | 0.0159336 | 1.955915e-01 | 1.5298201 | 1.629314 | 1.5282530 | 1.569811 |
| USDJPY | fGARCH.APARCH | 0.6351351 | 90 | 0.0747748 | 1.918659e+04 | -35.6149014 | -35.481562 | -35.6176305 | -35.561309 |
| USDJPY | fGARCH.GJRGARCH | 0.0120460 | 501 | 0.0159200 | 1.907374e-01 | 1.5495703 | 1.649064 | 1.5480031 | 1.589562 |
| USDJPY | fGARCH.ALLGARCH | 0.0155991 | 197 | 0.0404508 | 5.785243e+03 | -9.0125188 | -8.878054 | -9.0152765 | -8.958471 |
| USDJPY | eGARCH | 0.0182199 | 328 | 0.0242791 | 2.129471e+00 | 1.6186471 | 1.726383 | 1.6168234 | 1.661952 |
| USDJPY | gjrGARCH | 0.0098006 | 501 | 0.0159289 | 1.939950e-01 | 1.5445695 | 1.644063 | 1.5430024 | 1.584561 |
| USDJPY | apARCH | 0.8924450 | 76 | 0.0817778 | 1.560462e+05 | -122.2742164 | -122.136397 | -122.2771176 | -122.218824 |
| USDJPY | iGARCH | 0.0111525 | 501 | 0.0159235 | 1.886136e-01 | 1.5534422 | 1.625652 | 1.5525757 | 1.582467 |
| USDJPY | csGARCH | 0.0250917 | 501 | 0.0158679 | 1.773992e-01 | 1.5655868 | 1.678722 | 1.5635901 | 1.611061 |
6.4.1.1 : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 0.0020746 | 3507 | 0.0022800 | 12.04987 | -6.515680 | -6.435389 | -6.516711 | -6.483406 |
| fGARCH.GARCH | 0.0018459 | 3507 | 0.0022801 | 12.04976 | -6.514930 | -6.434639 | -6.515962 | -6.482657 |
| fGARCH.TGARCH | 0.0023210 | 3507 | 0.0022798 | 11.85924 | -6.351544 | -6.257605 | -6.352932 | -6.313785 |
| fGARCH.AVGARCH | 0.0109029 | 209 | 0.0381732 | 58.57421 | -6.010457 | -5.900663 | -6.012343 | -5.966325 |
| fGARCH.NGARCH | 0.0031232 | 3507 | 0.0022794 | 6382.53104 | -18.208671 | -18.114732 | -18.210059 | -18.170912 |
| fGARCH.NAGARCH | 0.0013454 | 3507 | 0.0022804 | 34.19263 | -6.414587 | -6.320648 | -6.415975 | -6.376828 |
| fGARCH.APARCH | 0.0461381 | 1239 | 0.0063823 | 5704.31360 | -19.398802 | -19.292282 | -19.400559 | -19.355985 |
| fGARCH.GJRGARCH | 0.0019792 | 3507 | 0.0022800 | 12.14498 | -6.512905 | -6.418966 | -6.514292 | -6.475146 |
| fGARCH.ALLGARCH | 0.0021225 | 1448 | 0.0055219 | 1717.03301 | -10.226987 | -10.106163 | -10.229229 | -10.178420 |
| eGARCH | 0.0028265 | 2301 | 0.0034743 | 15.05330 | -6.632755 | -6.537491 | -6.634190 | -6.594463 |
| gjrGARCH | 0.0016747 | 3507 | 0.0022802 | 12.07362 | -6.534549 | -6.440610 | -6.535937 | -6.496790 |
| apARCH | 0.1265412 | 536 | 0.0144532 | 23710.50701 | -24.354497 | -24.244516 | -24.356385 | -24.310290 |
| iGARCH | 0.0019789 | 3507 | 0.0022800 | 12.10561 | -6.462297 | -6.395655 | -6.463026 | -6.435510 |
| csGARCH | 0.0039468 | 3507 | 0.0022789 | 12.10702 | -6.475489 | -6.367902 | -6.477285 | -6.432244 |
6.4.1.2 : Table summary
| Model | n |
|---|---|
| sGARCH | 2 |
| fGARCH.GARCH | 2 |
| fGARCH.TGARCH | 2 |
| fGARCH.NGARCH | 47 |
| fGARCH.NAGARCH | 9 |
| fGARCH.APARCH | 1 |
| fGARCH.GJRGARCH | 4 |
| fGARCH.ALLGARCH | 4 |
| eGARCH | 5 |
| gjrGARCH | 3 |
| apARCH | 3 |
| iGARCH | 9 |
| csGARCH | 4 |
6.4.1.3 : Table summary
## selected models' filtered lowest price.
lp <- united.fx2 %>%
separate(Type, c('Cur', 'Type')) %>%
dplyr::filter(Type == 'Lo') %>% dplyr::select(-Cur, -Type)
acc <- lp %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 3.000000e-07 | 559 | 1.431130e-02 | 1.635410e-01 | -7.474533 | -7.395006 | -7.475542 | -7.442566 |
| USDAUD | fGARCH.GARCH | 3.000000e-07 | 559 | 1.431130e-02 | 1.636406e-01 | -7.474507 | -7.394980 | -7.475517 | -7.442540 |
| USDAUD | fGARCH.TGARCH | 2.400000e-06 | 559 | 1.431130e-02 | 8.492932e-01 | -7.196383 | -7.103202 | -7.197746 | -7.158928 |
| USDAUD | fGARCH.NGARCH | 3.845000e-03 | 559 | 1.429750e-02 | 1.444165e+04 | -38.661575 | -38.568394 | -38.662937 | -38.624119 |
| USDAUD | fGARCH.NAGARCH | 6.000000e-07 | 559 | 1.431130e-02 | 1.863712e-01 | -7.474842 | -7.381661 | -7.476204 | -7.437387 |
| USDAUD | fGARCH.GJRGARCH | 1.200000e-06 | 559 | 1.431130e-02 | 1.843323e-01 | -7.468833 | -7.375653 | -7.470196 | -7.431378 |
| USDAUD | gjrGARCH | 1.200000e-06 | 559 | 1.431130e-02 | 1.851478e-01 | -7.473855 | -7.380674 | -7.475218 | -7.436400 |
| USDAUD | iGARCH | 1.200000e-06 | 559 | 1.431130e-02 | 1.800006e-01 | -7.472048 | -7.406174 | -7.472758 | -7.445569 |
| USDAUD | csGARCH | 6.000000e-07 | 559 | 1.431130e-02 | 1.809284e-01 | -7.453969 | -7.347135 | -7.455738 | -7.411026 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 3.130009e-01 | -8.483968 | -8.402594 | -8.485037 | -8.451259 |
| USDEUR | fGARCH.GARCH | 2.000000e-07 | 559 | 1.431130e-02 | 3.132199e-01 | -8.483714 | -8.402340 | -8.484783 | -8.451005 |
| USDEUR | fGARCH.TGARCH | 7.000000e-07 | 559 | 1.431130e-02 | 5.616512e-01 | -8.289653 | -8.194626 | -8.291083 | -8.251456 |
| USDEUR | fGARCH.NGARCH | 3.480575e+33 | 559 | -1.245286e+31 | 1.389069e+04 | -31.661434 | -31.566406 | -31.662863 | -31.623236 |
| USDEUR | fGARCH.NAGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 1.216795e+02 | -8.027114 | -7.932086 | -8.028543 | -7.988917 |
| USDEUR | fGARCH.GJRGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 3.127732e-01 | -8.488332 | -8.393304 | -8.489761 | -8.450135 |
| USDEUR | gjrGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 3.145620e-01 | -8.503633 | -8.408605 | -8.505062 | -8.465435 |
| USDEUR | iGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 3.095536e-01 | -8.481167 | -8.413446 | -8.481930 | -8.453946 |
| USDEUR | csGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 3.063827e-01 | -8.462086 | -8.353405 | -8.463929 | -8.418401 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 0.000000e+00 | 559 | 1.431130e-02 | 8.946890e-02 | -9.161118 | -9.082595 | -9.162118 | -9.129556 |
| USDGBP | fGARCH.GARCH | 2.000000e-07 | 559 | 1.431130e-02 | 9.100420e-02 | -9.158372 | -9.079849 | -9.159371 | -9.126810 |
| USDGBP | fGARCH.TGARCH | 2.148452e+144 | 559 | -7.686770e+141 | 2.497319e+02 | -8.248833 | -8.156670 | -8.250181 | -8.211788 |
| USDGBP | fGARCH.NGARCH | 4.480000e-05 | 559 | 1.431110e-02 | 1.052975e+03 | -11.191570 | -11.099407 | -11.192918 | -11.154526 |
| USDGBP | fGARCH.NAGARCH | 0.000000e+00 | 559 | 1.431130e-02 | 1.958370e+01 | -8.978418 | -8.886255 | -8.979766 | -8.941373 |
| USDGBP | fGARCH.GJRGARCH | 0.000000e+00 | 559 | 1.431130e-02 | 9.174750e-02 | -9.172810 | -9.080647 | -9.174158 | -9.135766 |
| USDGBP | gjrGARCH | 0.000000e+00 | 559 | 1.431130e-02 | 9.343310e-02 | -9.182518 | -9.090355 | -9.183865 | -9.145473 |
| USDGBP | iGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 9.246110e-02 | -9.157658 | -9.092774 | -9.158362 | -9.131578 |
| USDGBP | csGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 8.889350e-02 | -9.139872 | -9.034069 | -9.141621 | -9.097345 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 2.144000e-04 | 559 | 1.431050e-02 | 3.752016e-01 | -7.774831 | -7.694935 | -7.775843 | -7.742716 |
| USDCHF | fGARCH.GARCH | 2.144000e-04 | 559 | 1.431050e-02 | 3.749116e-01 | -7.774567 | -7.694670 | -7.775579 | -7.742451 |
| USDCHF | fGARCH.TGARCH | 1.983000e-04 | 559 | 1.431060e-02 | 2.708022e-01 | -7.708955 | -7.615403 | -7.710322 | -7.671351 |
| USDCHF | fGARCH.NGARCH | 1.423492e+01 | 559 | -3.661870e-02 | 1.359109e+03 | -9.977072 | -9.883520 | -9.978439 | -9.939467 |
| USDCHF | fGARCH.NAGARCH | 2.094000e-04 | 559 | 1.431050e-02 | 3.677811e-01 | -7.797744 | -7.704192 | -7.799111 | -7.760140 |
| USDCHF | fGARCH.GJRGARCH | 2.105000e-04 | 559 | 1.431050e-02 | 3.267764e-01 | -7.802842 | -7.709290 | -7.804209 | -7.765237 |
| USDCHF | gjrGARCH | 2.099000e-04 | 559 | 1.431050e-02 | 3.288728e-01 | -7.819683 | -7.726131 | -7.821050 | -7.782079 |
| USDCHF | iGARCH | 1.074700e-03 | 559 | 1.430740e-02 | 7.945705e-01 | -7.544803 | -7.478562 | -7.545514 | -7.518176 |
| USDCHF | csGARCH | 5.459000e-04 | 559 | 1.430930e-02 | 5.454560e-01 | -7.668232 | -7.561024 | -7.670007 | -7.625138 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 1.916711e-01 | -8.088370 | -8.013856 | -8.089250 | -8.058418 |
| USDCAD | fGARCH.GARCH | 2.000000e-07 | 559 | 1.431130e-02 | 1.918087e-01 | -8.088324 | -8.013809 | -8.089204 | -8.058372 |
| USDCAD | fGARCH.TGARCH | 9.000000e-07 | 559 | 1.431130e-02 | 5.853322e-01 | -7.839604 | -7.751436 | -7.840818 | -7.804164 |
| USDCAD | fGARCH.NGARCH | 2.000000e-06 | 559 | 1.431130e-02 | 4.591249e+03 | -14.552735 | -14.464567 | -14.553949 | -14.517295 |
| USDCAD | fGARCH.NAGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 1.924688e-01 | -8.099150 | -8.010982 | -8.100364 | -8.063710 |
| USDCAD | fGARCH.GJRGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 1.918669e-01 | -8.089459 | -8.001291 | -8.090673 | -8.054019 |
| USDCAD | gjrGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 1.920297e-01 | -8.095753 | -8.007585 | -8.096967 | -8.060313 |
| USDCAD | iGARCH | 4.000000e-07 | 559 | 1.431130e-02 | 1.919475e-01 | -8.088169 | -8.027308 | -8.088769 | -8.063705 |
| USDCAD | csGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 1.907060e-01 | -8.072317 | -7.970495 | -8.073917 | -8.031388 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 2.262900e-03 | 559 | 1.430320e-02 | 3.480297e+00 | -6.119973 | -6.035698 | -6.121100 | -6.086099 |
| USDCNY | fGARCH.GARCH | 1.389700e-03 | 559 | 1.430630e-02 | 3.485897e+00 | -6.119032 | -6.034756 | -6.120159 | -6.085157 |
| USDCNY | fGARCH.TGARCH | 3.759400e-03 | 559 | 1.429780e-02 | 3.134419e+00 | -6.069236 | -5.971318 | -6.070735 | -6.029878 |
| USDCNY | fGARCH.NGARCH | 8.685799e+02 | 559 | -3.093309e+00 | 2.069808e+04 | -44.681562 | -44.583644 | -44.683060 | -44.642204 |
| USDCNY | fGARCH.NAGARCH | 1.306003e+03 | 559 | -4.658330e+00 | 1.045896e+02 | -5.276130 | -5.178212 | -5.277628 | -5.236771 |
| USDCNY | fGARCH.GJRGARCH | 7.771340e-02 | 559 | 1.403320e-02 | 2.347145e+01 | -5.865308 | -5.767390 | -5.866807 | -5.825950 |
| USDCNY | gjrGARCH | 2.022800e-03 | 559 | 1.430400e-02 | 3.419189e+00 | -6.150783 | -6.052865 | -6.152281 | -6.111424 |
| USDCNY | iGARCH | 2.897400e-03 | 559 | 1.430090e-02 | 3.806027e+00 | -6.006029 | -5.935396 | -6.006838 | -5.977638 |
| USDCNY | csGARCH | 2.429700e-03 | 559 | 1.430260e-02 | 3.951922e+00 | -6.038950 | -5.927390 | -6.040872 | -5.994108 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 1.185130e-02 | 559 | 1.426890e-02 | 1.932612e-01 | 1.505986 | 1.592135 | 1.504786 | 1.540614 |
| USDJPY | fGARCH.GARCH | 1.135080e-02 | 559 | 1.427070e-02 | 1.928677e-01 | 1.506372 | 1.592520 | 1.505171 | 1.540999 |
| USDJPY | fGARCH.TGARCH | 1.251800e-02 | 559 | 1.426650e-02 | 2.640584e-01 | 1.532982 | 1.632773 | 1.531404 | 1.573093 |
| USDJPY | fGARCH.NGARCH | 1.698360e-02 | 559 | 1.425050e-02 | 6.624668e+03 | -11.603252 | -11.503462 | -11.604831 | -11.563142 |
| USDJPY | fGARCH.NAGARCH | 8.457900e-03 | 559 | 1.428100e-02 | 2.019745e-01 | 1.480656 | 1.580447 | 1.479078 | 1.520767 |
| USDJPY | fGARCH.GJRGARCH | 1.166140e-02 | 559 | 1.426950e-02 | 1.977772e-01 | 1.500435 | 1.600226 | 1.498857 | 1.540546 |
| USDJPY | gjrGARCH | 9.850400e-03 | 559 | 1.427600e-02 | 2.015961e-01 | 1.494715 | 1.594506 | 1.493136 | 1.534826 |
| USDJPY | iGARCH | 1.079900e-02 | 559 | 1.427260e-02 | 1.960169e-01 | 1.504274 | 1.576780 | 1.503399 | 1.533418 |
| USDJPY | csGARCH | 2.392930e-02 | 559 | 1.422570e-02 | 1.855740e-01 | 1.516742 | 1.630175 | 1.514733 | 1.562337 |
6.4.2.1A : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 2.047000e-03 | 3913 | 2.043400e-03 | 12.16584 | -6.513830 | -6.433221 | -6.514872 | -6.481428 |
| fGARCH.GARCH | 1.850800e-03 | 3913 | 2.043500e-03 | 12.16547 | -6.513163 | -6.432555 | -6.514206 | -6.480762 |
| fGARCH.TGARCH | 3.069217e+143 | 3913 | -1.568728e+140 | 47.10154 | -6.259955 | -6.165698 | -6.261354 | -6.222067 |
| fGARCH.NGARCH | 4.972251e+32 | 3913 | -2.541401e+29 | 9136.97551 | -23.189886 | -23.095629 | -23.191285 | -23.151999 |
| fGARCH.NAGARCH | 1.865731e+02 | 3913 | -9.331620e-02 | 46.48641 | -6.310392 | -6.216134 | -6.311791 | -6.272504 |
| fGARCH.GJRGARCH | 1.279810e-02 | 3913 | 2.037900e-03 | 15.06350 | -6.483879 | -6.389621 | -6.485278 | -6.445991 |
| gjrGARCH | 1.726400e-03 | 3913 | 2.043600e-03 | 12.17306 | -6.533073 | -6.438816 | -6.534472 | -6.495186 |
| iGARCH | 2.110400e-03 | 3913 | 2.043400e-03 | 12.20295 | -6.463657 | -6.396697 | -6.464396 | -6.436742 |
| csGARCH | 3.843700e-03 | 3913 | 2.042500e-03 | 12.21308 | -6.474098 | -6.366192 | -6.475907 | -6.430724 |
6.4.2.1B : Table summary
| Model | n |
|---|---|
| sGARCH | 1 |
| fGARCH.GARCH | 1 |
| fGARCH.TGARCH | 2 |
| fGARCH.NGARCH | 41 |
| fGARCH.NAGARCH | 7 |
| fGARCH.GJRGARCH | 2 |
| gjrGARCH | 1 |
| iGARCH | 6 |
| csGARCH | 3 |
6.4.2.1C : Table summary
## selected models' filtered lowest price.
lp <- united.fx3 %>%
separate(Type, c('Cur', 'Type')) %>%
dplyr::filter(Type == 'Lo') %>% dplyr::select(-Cur, -Type)
acc <- lp %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 0.0000003 | 488 | 0.0163934 | 1.725312e-01 | -7.452467 | -7.374435 | -7.453430 | -7.421101 |
| USDAUD | fGARCH.GARCH | 0.0000003 | 488 | 0.0163934 | 1.726293e-01 | -7.452413 | -7.374382 | -7.453377 | -7.421048 |
| USDAUD | fGARCH.TGARCH | 0.0000024 | 488 | 0.0163934 | 8.223861e-01 | -7.176764 | -7.085079 | -7.178075 | -7.139910 |
| USDAUD | fGARCH.NGARCH | 0.0000023 | 488 | 0.0163934 | 1.444521e+04 | -40.086289 | -39.994603 | -40.087600 | -40.049435 |
| USDAUD | fGARCH.NAGARCH | 0.0000006 | 488 | 0.0163934 | 1.979164e-01 | -7.451847 | -7.360162 | -7.453158 | -7.414993 |
| USDAUD | fGARCH.GJRGARCH | 0.0000013 | 488 | 0.0163934 | 1.959013e-01 | -7.446020 | -7.354335 | -7.447331 | -7.409166 |
| USDAUD | gjrGARCH | 0.0000013 | 488 | 0.0163934 | 1.968724e-01 | -7.451272 | -7.359587 | -7.452583 | -7.414418 |
| USDAUD | iGARCH | 0.0000013 | 488 | 0.0163934 | 1.913234e-01 | -7.449519 | -7.385141 | -7.450189 | -7.423641 |
| USDAUD | csGARCH | 0.0000007 | 488 | 0.0163934 | 1.921225e-01 | -7.431224 | -7.325885 | -7.432936 | -7.388882 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 0.0000002 | 488 | 0.0163934 | 2.857214e-01 | -8.417592 | -8.336519 | -8.418653 | -8.385004 |
| USDEUR | fGARCH.GARCH | 0.0000002 | 488 | 0.0163934 | 2.861404e-01 | -8.417432 | -8.336360 | -8.418494 | -8.384844 |
| USDEUR | fGARCH.TGARCH | 0.0000007 | 488 | 0.0163934 | 5.406500e-01 | -8.211931 | -8.117205 | -8.213351 | -8.173854 |
| USDEUR | fGARCH.NGARCH | 0.0000070 | 488 | 0.0163934 | 1.394235e+04 | -31.829083 | -31.734357 | -31.830503 | -31.791007 |
| USDEUR | fGARCH.NAGARCH | 0.0000002 | 488 | 0.0163934 | 1.392042e+02 | -7.893397 | -7.798671 | -7.894817 | -7.855321 |
| USDEUR | fGARCH.GJRGARCH | 0.0000002 | 488 | 0.0163934 | 2.863780e-01 | -8.422621 | -8.327896 | -8.424042 | -8.384545 |
| USDEUR | gjrGARCH | 0.0000002 | 488 | 0.0163934 | 2.902450e-01 | -8.439312 | -8.344587 | -8.440733 | -8.401236 |
| USDEUR | iGARCH | 0.0000002 | 488 | 0.0163934 | 2.820781e-01 | -8.414689 | -8.347270 | -8.415445 | -8.387589 |
| USDEUR | csGARCH | 0.0000002 | 488 | 0.0163934 | 2.801280e-01 | -8.396414 | -8.288035 | -8.398247 | -8.352850 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 0.0000000 | 488 | 0.0163934 | 7.831430e-02 | -9.121841 | -9.045012 | -9.122789 | -9.090960 |
| USDGBP | fGARCH.GARCH | 0.0000000 | 488 | 0.0163934 | 7.822300e-02 | -9.121683 | -9.044854 | -9.122631 | -9.090802 |
| USDGBP | fGARCH.TGARCH | 0.0000001 | 488 | 0.0163934 | 2.528842e-01 | -8.893066 | -8.802598 | -8.894356 | -8.856703 |
| USDGBP | fGARCH.NGARCH | 0.0000001 | 488 | 0.0163934 | 4.578560e+02 | -9.949566 | -9.859098 | -9.950856 | -9.913203 |
| USDGBP | fGARCH.NAGARCH | 0.0000000 | 488 | 0.0163934 | 2.236856e+01 | -8.918755 | -8.828287 | -8.920044 | -8.882392 |
| USDGBP | fGARCH.GJRGARCH | 0.0000000 | 488 | 0.0163934 | 8.179240e-02 | -9.134428 | -9.043960 | -9.135718 | -9.098065 |
| USDGBP | gjrGARCH | 0.0000000 | 488 | 0.0163934 | 8.386380e-02 | -9.144139 | -9.053671 | -9.145428 | -9.107776 |
| USDGBP | iGARCH | 0.0000001 | 488 | 0.0163934 | 7.960610e-02 | -9.120698 | -9.057507 | -9.121357 | -9.095299 |
| USDGBP | csGARCH | 0.0000000 | 488 | 0.0163934 | 7.839250e-02 | -9.101445 | -8.997338 | -9.103130 | -9.059600 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 0.0000087 | 488 | 0.0163934 | 3.627975e-01 | -7.721654 | -7.641575 | -7.722671 | -7.689465 |
| USDCHF | fGARCH.GARCH | 0.0000087 | 488 | 0.0163934 | 3.626083e-01 | -7.721453 | -7.641374 | -7.722471 | -7.689264 |
| USDCHF | fGARCH.TGARCH | 0.0000005 | 488 | 0.0163934 | 2.569832e-01 | -7.659628 | -7.565892 | -7.661000 | -7.621949 |
| USDCHF | fGARCH.NGARCH | 0.0000071 | 488 | 0.0163934 | 8.731373e+02 | -9.053339 | -8.959604 | -9.054712 | -9.015660 |
| USDCHF | fGARCH.NAGARCH | 0.0000049 | 488 | 0.0163934 | 3.590547e-01 | -7.745817 | -7.652081 | -7.747189 | -7.708138 |
| USDCHF | fGARCH.GJRGARCH | 0.0000051 | 488 | 0.0163934 | 3.130331e-01 | -7.752129 | -7.658393 | -7.753501 | -7.714450 |
| USDCHF | gjrGARCH | 0.0000067 | 488 | 0.0163934 | 3.172775e-01 | -7.770415 | -7.676680 | -7.771788 | -7.732737 |
| USDCHF | iGARCH | 0.0003091 | 488 | 0.0163922 | 7.817977e-01 | -7.485358 | -7.418934 | -7.486073 | -7.458658 |
| USDCHF | csGARCH | 0.0000865 | 488 | 0.0163931 | 5.068516e-01 | -7.625923 | -7.518532 | -7.627705 | -7.582756 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 0.0000001 | 488 | 0.0163934 | 2.040959e-01 | -8.070325 | -7.996607 | -8.071180 | -8.040693 |
| USDCAD | fGARCH.GARCH | 0.0000001 | 488 | 0.0163934 | 2.042526e-01 | -8.070255 | -7.996537 | -8.071110 | -8.040623 |
| USDCAD | fGARCH.TGARCH | 0.0000010 | 488 | 0.0163934 | 6.302208e-01 | -7.818137 | -7.730766 | -7.819323 | -7.783017 |
| USDCAD | fGARCH.NGARCH | 0.0000023 | 488 | 0.0163934 | 5.230717e+03 | -15.739612 | -15.652241 | -15.740798 | -15.704493 |
| USDCAD | fGARCH.NAGARCH | 0.0000001 | 488 | 0.0163934 | 2.046421e-01 | -8.080122 | -7.992751 | -8.081308 | -8.045003 |
| USDCAD | fGARCH.GJRGARCH | 0.0000001 | 488 | 0.0163934 | 2.043379e-01 | -8.071354 | -7.983983 | -8.072540 | -8.036234 |
| USDCAD | gjrGARCH | 0.0000001 | 488 | 0.0163934 | 2.047260e-01 | -8.078045 | -7.990674 | -8.079231 | -8.042925 |
| USDCAD | iGARCH | 0.0000004 | 488 | 0.0163934 | 2.045283e-01 | -8.070094 | -8.010029 | -8.070672 | -8.045950 |
| USDCAD | csGARCH | 0.0000002 | 488 | 0.0163934 | 2.029442e-01 | -8.053908 | -7.952884 | -8.055478 | -8.013300 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 0.0022246 | 488 | 0.0163843 | 2.738811e+00 | -6.414457 | -6.328884 | -6.415617 | -6.380061 |
| USDCNY | fGARCH.GARCH | 0.0012478 | 488 | 0.0163883 | 2.747907e+00 | -6.412755 | -6.327181 | -6.413915 | -6.378359 |
| USDCNY | fGARCH.TGARCH | 0.0040670 | 488 | 0.0163768 | 2.742650e+00 | -6.319874 | -6.220659 | -6.321410 | -6.279995 |
| USDCNY | fGARCH.NGARCH | 0.0044083 | 488 | 0.0163754 | 7.063666e+02 | -7.646877 | -7.547663 | -7.648414 | -7.606998 |
| USDCNY | fGARCH.NAGARCH | 0.0007926 | 488 | 0.0163902 | 3.734072e+00 | -6.363653 | -6.264438 | -6.365189 | -6.323774 |
| USDCNY | fGARCH.GJRGARCH | 0.0018272 | 488 | 0.0163860 | 3.357318e+00 | -6.345049 | -6.245834 | -6.346586 | -6.305170 |
| USDCNY | gjrGARCH | 0.0019421 | 488 | 0.0163855 | 2.742138e+00 | -6.436638 | -6.337424 | -6.438175 | -6.396759 |
| USDCNY | iGARCH | 0.0024425 | 488 | 0.0163834 | 3.245522e+00 | -6.284312 | -6.212380 | -6.285149 | -6.255399 |
| USDCNY | csGARCH | 0.0025086 | 488 | 0.0163832 | 3.304587e+00 | -6.323511 | -6.210655 | -6.325476 | -6.278148 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 0.0132737 | 488 | 0.0163390 | 1.905605e-01 | 1.546984 | 1.633806 | 1.545763 | 1.581882 |
| USDJPY | fGARCH.GARCH | 0.0126977 | 488 | 0.0163414 | 1.903570e-01 | 1.547232 | 1.634055 | 1.546011 | 1.582130 |
| USDJPY | fGARCH.TGARCH | 0.0139856 | 488 | 0.0163361 | 2.694663e-01 | 1.576002 | 1.676466 | 1.574400 | 1.616384 |
| USDJPY | fGARCH.NGARCH | 0.0190688 | 488 | 0.0163153 | 6.711076e+03 | -11.550041 | -11.449577 | -11.551643 | -11.509659 |
| USDJPY | fGARCH.NAGARCH | 0.0093622 | 488 | 0.0163551 | 2.008009e-01 | 1.521855 | 1.622319 | 1.520253 | 1.562236 |
| USDJPY | fGARCH.GJRGARCH | 0.0128591 | 488 | 0.0163407 | 1.956559e-01 | 1.541469 | 1.641933 | 1.539867 | 1.581850 |
| USDJPY | gjrGARCH | 0.0109308 | 488 | 0.0163486 | 1.991889e-01 | 1.536451 | 1.636915 | 1.534849 | 1.576832 |
| USDJPY | iGARCH | 0.0120699 | 488 | 0.0163440 | 1.936601e-01 | 1.545427 | 1.618607 | 1.544533 | 1.574842 |
| USDJPY | csGARCH | 0.0271353 | 488 | 0.0162822 | 1.819636e-01 | 1.558096 | 1.672201 | 1.556061 | 1.603960 |
6.4.2.2A : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 0.0022154 | 3416 | 0.0023406 | 12.02966 | -6.521622 | -6.441318 | -6.522654 | -6.489343 |
| fGARCH.GARCH | 0.0019935 | 3416 | 0.0023408 | 12.03129 | -6.521251 | -6.440948 | -6.522284 | -6.488973 |
| fGARCH.TGARCH | 0.0025796 | 3416 | 0.0023404 | 11.83219 | -6.357628 | -6.263676 | -6.359017 | -6.319864 |
| fGARCH.NGARCH | 0.0033565 | 3416 | 0.0023400 | 6192.07254 | -17.979258 | -17.885306 | -17.980646 | -17.941494 |
| fGARCH.NAGARCH | 0.0014515 | 3416 | 0.0023411 | 34.76267 | -6.418819 | -6.324867 | -6.420208 | -6.381055 |
| fGARCH.GJRGARCH | 0.0020990 | 3416 | 0.0023407 | 12.12712 | -6.518590 | -6.424638 | -6.519979 | -6.480826 |
| gjrGARCH | 0.0018402 | 3416 | 0.0023408 | 12.05327 | -6.540482 | -6.446529 | -6.541870 | -6.502717 |
| iGARCH | 0.0021176 | 3416 | 0.0023407 | 12.08840 | -6.468463 | -6.401808 | -6.469193 | -6.441671 |
| csGARCH | 0.0042474 | 3416 | 0.0023394 | 12.08889 | -6.482047 | -6.374447 | -6.483844 | -6.438796 |
6.4.2.2B : Table summary
| Model | n |
|---|---|
6.4.2.2C : Table summary
## filtered bias closing price.
cl <- fx %>% separate(Type, c('Cur', 'Type')) %>%
dplyr::filter(Type == 'Cl') %>%
dplyr::select(-Cur, -Type)
ntmID <- cl %>% dplyr::filter(se == 1) %>% .$Date %>% unlist %>% sort
acc <- cl %>% dplyr::filter(!Date %in% ntmID & Date %in% ntimeID2) %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 0.0000008 | 553 | 0.0144665 | 1.567179e-01 | -7.286875 | -7.205357 | -7.287939 | -7.254108 |
| USDAUD | fGARCH.GARCH | 0.0000008 | 553 | 0.0144665 | 1.566690e-01 | -7.287138 | -7.205620 | -7.288203 | -7.254371 |
| USDAUD | fGARCH.TGARCH | 0.0000031 | 553 | 0.0144665 | 4.730421e-01 | -7.096140 | -7.000968 | -7.097565 | -7.057885 |
| USDAUD | fGARCH.AVGARCH | 0.0000001 | 54 | 0.1481481 | 4.757932e+00 | -7.310062 | -7.196754 | -7.312065 | -7.264516 |
| USDAUD | fGARCH.NGARCH | 0.0000126 | 553 | 0.0144665 | 1.133613e+04 | -26.053368 | -25.958196 | -26.054793 | -26.015112 |
| USDAUD | fGARCH.NAGARCH | 0.0000007 | 553 | 0.0144665 | 1.074984e+02 | -6.856085 | -6.760913 | -6.857510 | -6.817830 |
| USDAUD | fGARCH.APARCH | 0.0000002 | 222 | 0.0360360 | 2.504730e-01 | -7.326566 | -7.219561 | -7.328353 | -7.283552 |
| USDAUD | fGARCH.GJRGARCH | 0.0000007 | 553 | 0.0144665 | 1.594684e-01 | -7.291695 | -7.196523 | -7.293120 | -7.253439 |
| USDAUD | fGARCH.ALLGARCH | 0.0000014 | 123 | 0.0650406 | 2.753927e+03 | -12.379895 | -12.249724 | -12.382509 | -12.327570 |
| USDAUD | eGARCH | 0.0000010 | 376 | 0.0212766 | 8.348472e+00 | -7.314903 | -7.220515 | -7.316315 | -7.276962 |
| USDAUD | gjrGARCH | 0.0000007 | 553 | 0.0144665 | 1.625273e-01 | -7.299096 | -7.203924 | -7.300521 | -7.260840 |
| USDAUD | apARCH | 0.0000003 | 83 | 0.0963855 | 3.702800e-03 | -7.754844 | -7.637342 | -7.757004 | -7.707612 |
| USDAUD | iGARCH | 0.0000008 | 553 | 0.0144665 | 1.560441e-01 | -7.291631 | -7.223766 | -7.292388 | -7.264352 |
| USDAUD | csGARCH | 0.0000011 | 553 | 0.0144665 | 1.594027e-01 | -7.270102 | -7.161276 | -7.271941 | -7.226358 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 0.0000004 | 553 | 0.0144665 | 3.417287e-01 | -8.263680 | -8.180259 | -8.264786 | -8.230148 |
| USDEUR | fGARCH.GARCH | 0.0000004 | 553 | 0.0144665 | 3.413142e-01 | -8.263324 | -8.179902 | -8.264429 | -8.229791 |
| USDEUR | fGARCH.TGARCH | 0.0000014 | 553 | 0.0144665 | 5.919376e-01 | -8.147051 | -8.049976 | -8.148524 | -8.108030 |
| USDEUR | fGARCH.AVGARCH | 0.0000000 | 28 | 0.2857143 | 2.975550e-02 | -8.033852 | -7.933416 | -8.035424 | -7.993481 |
| USDEUR | fGARCH.NGARCH | 0.0000024 | 553 | 0.0144665 | 9.210761e+03 | -23.366813 | -23.269738 | -23.368286 | -23.327792 |
| USDEUR | fGARCH.NAGARCH | 0.0000003 | 553 | 0.0144665 | 3.498244e-01 | -8.279410 | -8.182334 | -8.280883 | -8.240389 |
| USDEUR | fGARCH.APARCH | 0.0000000 | 95 | 0.0842105 | 1.095022e-01 | -7.889880 | -7.789674 | -7.891430 | -7.849601 |
| USDEUR | fGARCH.GJRGARCH | 0.0000003 | 553 | 0.0144665 | 3.501579e-01 | -8.279866 | -8.182791 | -8.281340 | -8.240845 |
| USDEUR | fGARCH.ALLGARCH | 0.0000001 | 234 | 0.0341880 | 2.068350e-02 | -8.227210 | -8.105537 | -8.229467 | -8.178300 |
| USDEUR | eGARCH | 0.0000010 | 378 | 0.0211640 | 8.604671e-01 | -8.483194 | -8.384282 | -8.484728 | -8.443434 |
| USDEUR | gjrGARCH | 0.0000004 | 553 | 0.0144665 | 3.546392e-01 | -8.291377 | -8.194302 | -8.292851 | -8.252357 |
| USDEUR | apARCH | 0.0000000 | 83 | 0.0963855 | 3.218000e-04 | -8.094296 | -7.994747 | -8.095826 | -8.054281 |
| USDEUR | iGARCH | 0.0000011 | 553 | 0.0144665 | 3.456698e-01 | -8.262433 | -8.192664 | -8.263223 | -8.234388 |
| USDEUR | csGARCH | 0.0000011 | 553 | 0.0144665 | 3.364927e-01 | -8.246527 | -8.135798 | -8.248421 | -8.202018 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 0.0000002 | 553 | 0.0144665 | 1.126069e-01 | -8.979091 | -8.899689 | -8.980119 | -8.947176 |
| USDGBP | fGARCH.GARCH | 0.0000002 | 553 | 0.0144665 | 1.122041e-01 | -8.979613 | -8.900211 | -8.980641 | -8.947698 |
| USDGBP | fGARCH.TGARCH | 0.0000002 | 553 | 0.0144665 | 3.222083e-01 | -8.747429 | -8.654388 | -8.748809 | -8.710031 |
| USDGBP | fGARCH.AVGARCH | 0.0000000 | 36 | 0.2222222 | 1.055895e-01 | -8.932965 | -8.835728 | -8.934416 | -8.893883 |
| USDGBP | fGARCH.NGARCH | 0.0000010 | 553 | 0.0144665 | 6.548758e+03 | -19.215693 | -19.122651 | -19.217072 | -19.178295 |
| USDGBP | fGARCH.NAGARCH | 0.0000000 | 553 | 0.0144665 | 9.012670e-01 | -8.957831 | -8.864790 | -8.959211 | -8.920433 |
| USDGBP | fGARCH.APARCH | 0.0000000 | 222 | 0.0360360 | 2.130398e+03 | -13.830028 | -13.729929 | -13.831580 | -13.789793 |
| USDGBP | fGARCH.GJRGARCH | 0.0000000 | 553 | 0.0144665 | 1.177579e-01 | -8.996964 | -8.903922 | -8.998344 | -8.959566 |
| USDGBP | fGARCH.ALLGARCH | 0.0000000 | 235 | 0.0340426 | 2.550575e-01 | -8.804263 | -8.688556 | -8.806328 | -8.757754 |
| USDGBP | eGARCH | 0.0000001 | 377 | 0.0212202 | 1.398285e+02 | -8.399918 | -8.305335 | -8.401353 | -8.361900 |
| USDGBP | gjrGARCH | 0.0000001 | 553 | 0.0144665 | 1.239441e-01 | -9.010310 | -8.917269 | -9.011690 | -8.972913 |
| USDGBP | apARCH | 0.0000001 | 83 | 0.0963855 | 5.287600e-03 | -9.080626 | -8.981842 | -9.082127 | -9.040922 |
| USDGBP | iGARCH | 0.0000001 | 553 | 0.0144665 | 1.115696e-01 | -8.981865 | -8.916104 | -8.982595 | -8.955433 |
| USDGBP | csGARCH | 0.0000001 | 553 | 0.0144665 | 1.111786e-01 | -8.960961 | -8.854279 | -8.962745 | -8.918080 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 0.0000037 | 553 | 0.0144665 | 4.816688e-01 | -7.473136 | -7.390007 | -7.474246 | -7.439721 |
| USDCHF | fGARCH.GARCH | 0.0000038 | 553 | 0.0144665 | 4.822807e-01 | -7.473833 | -7.390704 | -7.474943 | -7.440418 |
| USDCHF | fGARCH.TGARCH | 0.0000015 | 553 | 0.0144665 | 4.099288e-01 | -7.535677 | -7.438892 | -7.537154 | -7.496773 |
| USDCHF | fGARCH.AVGARCH | 0.0000004 | 16 | 0.4999999 | 6.610170e-02 | -7.644302 | -7.533805 | -7.646256 | -7.599879 |
| USDCHF | fGARCH.NGARCH | 0.0000025 | 553 | 0.0144665 | 1.461934e+04 | -33.078817 | -32.982032 | -33.080294 | -33.039912 |
| USDCHF | fGARCH.NAGARCH | 0.0000018 | 553 | 0.0144665 | 5.104681e+01 | -6.817336 | -6.720551 | -6.818813 | -6.778431 |
| USDCHF | fGARCH.APARCH | 0.0000115 | 221 | 0.0361990 | 1.180703e+04 | -28.609921 | -28.500146 | -28.611791 | -28.565793 |
| USDCHF | fGARCH.GJRGARCH | 0.0000025 | 553 | 0.0144665 | 4.521690e-01 | -7.525262 | -7.428477 | -7.526738 | -7.486357 |
| USDCHF | fGARCH.ALLGARCH | 0.0000058 | 233 | 0.0343347 | 8.640537e+03 | -22.811057 | -22.686868 | -22.813426 | -22.761135 |
| USDCHF | eGARCH | 0.0000002 | 377 | 0.0212202 | 1.093293e-01 | -7.928576 | -7.827633 | -7.930187 | -7.887999 |
| USDCHF | gjrGARCH | 0.0000023 | 553 | 0.0144665 | 4.519408e-01 | -7.546989 | -7.450204 | -7.548466 | -7.508085 |
| USDCHF | apARCH | 0.0000000 | 82 | 0.0975610 | 1.717200e-03 | -7.800074 | -7.699678 | -7.801637 | -7.759716 |
| USDCHF | iGARCH | 0.0000038 | 553 | 0.0144665 | 5.365865e-01 | -7.451428 | -7.381955 | -7.452224 | -7.423502 |
| USDCHF | csGARCH | 0.0000037 | 553 | 0.0144665 | 4.889091e-01 | -7.457156 | -7.346715 | -7.459053 | -7.412762 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 0.0000003 | 553 | 0.0144665 | 1.978004e-01 | -7.989967 | -7.909208 | -7.991016 | -7.957505 |
| USDCAD | fGARCH.GARCH | 0.0000002 | 553 | 0.0144665 | 1.979657e-01 | -7.989644 | -7.908886 | -7.990693 | -7.957182 |
| USDCAD | fGARCH.TGARCH | 0.0000011 | 553 | 0.0144665 | 6.055084e-01 | -7.772578 | -7.678166 | -7.773985 | -7.734628 |
| USDCAD | fGARCH.AVGARCH | 0.0000001 | 42 | 0.1904762 | 4.624600e-02 | -8.215936 | -8.105061 | -8.217839 | -8.171368 |
| USDCAD | fGARCH.NGARCH | 0.0000041 | 553 | 0.0144665 | 1.052691e+04 | -26.876132 | -26.781720 | -26.877539 | -26.838182 |
| USDCAD | fGARCH.NAGARCH | 0.0000002 | 553 | 0.0144665 | 1.971210e-01 | -7.998770 | -7.904358 | -8.000177 | -7.960820 |
| USDCAD | fGARCH.APARCH | 0.0000005 | 218 | 0.0366972 | 1.582323e+03 | -10.837918 | -10.731394 | -10.839683 | -10.795098 |
| USDCAD | fGARCH.GJRGARCH | 0.0000002 | 553 | 0.0144665 | 2.013034e-01 | -7.997480 | -7.903068 | -7.998888 | -7.959530 |
| USDCAD | fGARCH.ALLGARCH | 0.0000001 | 234 | 0.0341880 | 7.720133e+03 | -21.615187 | -21.493985 | -21.617447 | -21.566466 |
| USDCAD | eGARCH | 0.0000001 | 376 | 0.0212766 | 4.835220e-02 | -8.212085 | -8.118818 | -8.213454 | -8.174594 |
| USDCAD | gjrGARCH | 0.0000003 | 553 | 0.0144665 | 2.000689e-01 | -8.004257 | -7.909845 | -8.005664 | -7.966307 |
| USDCAD | apARCH | 0.0000001 | 82 | 0.0975610 | 2.889700e-03 | -8.313931 | -8.202503 | -8.315856 | -8.269141 |
| USDCAD | iGARCH | 0.0000003 | 553 | 0.0144665 | 2.004687e-01 | -7.988559 | -7.921453 | -7.989304 | -7.961585 |
| USDCAD | csGARCH | 0.0000003 | 553 | 0.0144665 | 1.954402e-01 | -7.974476 | -7.866411 | -7.976294 | -7.931038 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 0.0000083 | 553 | 0.0144665 | 2.007894e-01 | -6.942489 | -6.853278 | -6.943742 | -6.906630 |
| USDCNY | fGARCH.GARCH | 0.0000080 | 553 | 0.0144665 | 2.004679e-01 | -6.942925 | -6.853714 | -6.944178 | -6.907067 |
| USDCNY | fGARCH.TGARCH | 0.0000094 | 553 | 0.0144665 | 7.885634e-01 | -6.719408 | -6.616554 | -6.721051 | -6.678066 |
| USDCNY | fGARCH.AVGARCH | 0.0000035 | 12 | 0.6666661 | 3.877637e-01 | -6.447781 | -6.312844 | -6.450517 | -6.393549 |
| USDCNY | fGARCH.NGARCH | 0.0000189 | 553 | 0.0144665 | 1.230313e+03 | -9.088979 | -8.986126 | -9.090623 | -9.047637 |
| USDCNY | fGARCH.NAGARCH | 0.0000080 | 553 | 0.0144665 | 2.145262e-01 | -6.957386 | -6.854533 | -6.959030 | -6.916044 |
| USDCNY | fGARCH.APARCH | 0.0000299 | 219 | 0.0365294 | 9.202970e+03 | -21.204215 | -21.076902 | -21.206666 | -21.153042 |
| USDCNY | fGARCH.GJRGARCH | 0.0000070 | 553 | 0.0144665 | 2.110097e-01 | -6.968106 | -6.865252 | -6.969749 | -6.926764 |
| USDCNY | fGARCH.ALLGARCH | 0.0000147 | 234 | 0.0341879 | 1.490172e+03 | -9.271460 | -9.129206 | -9.274506 | -9.214281 |
| USDCNY | eGARCH | 0.0000103 | 374 | 0.0213903 | 2.780878e-01 | -6.929065 | -6.821028 | -6.930866 | -6.885639 |
| USDCNY | gjrGARCH | 0.0000070 | 553 | 0.0144665 | 1.894521e-01 | -6.997001 | -6.894148 | -6.998644 | -6.955659 |
| USDCNY | apARCH | 0.0000423 | 83 | 0.0963845 | 2.148161e+04 | -22.816651 | -22.685707 | -22.819248 | -22.764021 |
| USDCNY | iGARCH | 0.0000090 | 553 | 0.0144665 | 2.121893e-01 | -6.930118 | -6.854550 | -6.931034 | -6.899744 |
| USDCNY | csGARCH | 0.0000067 | 553 | 0.0144665 | 2.182596e-01 | -6.958826 | -6.842330 | -6.960912 | -6.912000 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 0.0094092 | 553 | 0.0144325 | 1.720671e-01 | 1.733870 | 1.820897 | 1.732643 | 1.768851 |
| USDJPY | fGARCH.GARCH | 0.0093819 | 553 | 0.0144326 | 1.719134e-01 | 1.734063 | 1.821090 | 1.732836 | 1.769043 |
| USDJPY | fGARCH.TGARCH | 0.0064246 | 553 | 0.0144433 | 1.860764e-01 | 1.738223 | 1.838892 | 1.736614 | 1.778687 |
| USDJPY | fGARCH.AVGARCH | 0.0285310 | 42 | 0.1891176 | 1.650240e-02 | 1.153284 | 1.290785 | 1.150376 | 1.208549 |
| USDJPY | fGARCH.NGARCH | 0.0287785 | 553 | 0.0143625 | 9.071474e+03 | -16.464806 | -16.364136 | -16.466414 | -16.424342 |
| USDJPY | fGARCH.NAGARCH | 0.0058205 | 553 | 0.0144455 | 1.830371e-01 | 1.721374 | 1.822043 | 1.719765 | 1.761838 |
| USDJPY | fGARCH.APARCH | 0.0844555 | 98 | 0.0799091 | 1.055256e+04 | -17.772625 | -17.647116 | -17.775110 | -17.722180 |
| USDJPY | fGARCH.GJRGARCH | 0.0065264 | 553 | 0.0144429 | 1.783273e-01 | 1.730190 | 1.830860 | 1.728582 | 1.770654 |
| USDJPY | fGARCH.ALLGARCH | 1.3908392 | 205 | 0.0254552 | 1.043499e+04 | -17.705769 | -17.582823 | -17.708125 | -17.656351 |
| USDJPY | eGARCH | 0.0175706 | 375 | 0.0212396 | 3.962323e-01 | 1.761843 | 1.862994 | 1.760201 | 1.802501 |
| USDJPY | gjrGARCH | 0.0055060 | 553 | 0.0144466 | 1.862176e-01 | 1.718959 | 1.819629 | 1.717351 | 1.759423 |
| USDJPY | apARCH | 0.0516102 | 82 | 0.0963022 | 4.394985e+04 | -31.860717 | -31.729329 | -31.863416 | -31.807909 |
| USDJPY | iGARCH | 0.0096980 | 553 | 0.0144315 | 1.742472e-01 | 1.730081 | 1.803465 | 1.729182 | 1.759577 |
| USDJPY | csGARCH | 0.0092224 | 553 | 0.0144332 | 1.692324e-01 | 1.739656 | 1.853968 | 1.737613 | 1.785603 |
6.5.1.1 : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 0.0013461 | 3871 | 0.0020660 | 11.81224 | -6.457338 | -6.373843 | -6.458458 | -6.423777 |
| fGARCH.GARCH | 0.0013422 | 3871 | 0.0020660 | 11.81299 | -6.457488 | -6.373992 | -6.458607 | -6.423926 |
| fGARCH.TGARCH | 0.0009202 | 3871 | 0.0020662 | 11.69890 | -6.325723 | -6.228579 | -6.327211 | -6.286675 |
| fGARCH.AVGARCH | 0.0052103 | 230 | 0.0347373 | 13.80301 | -6.250398 | -6.136266 | -6.252444 | -6.204522 |
| fGARCH.NGARCH | 0.0041172 | 3871 | 0.0020645 | 8987.65380 | -22.020658 | -21.923514 | -22.022146 | -21.981610 |
| fGARCH.NAGARCH | 0.0008331 | 3871 | 0.0020662 | 34.23002 | -6.306492 | -6.209348 | -6.307980 | -6.267444 |
| fGARCH.APARCH | 0.0063984 | 1295 | 0.0061677 | 5056.42390 | -15.843399 | -15.732850 | -15.845304 | -15.798962 |
| fGARCH.GJRGARCH | 0.0009339 | 3871 | 0.0020662 | 11.84919 | -6.475598 | -6.378453 | -6.477085 | -6.436550 |
| fGARCH.ALLGARCH | 0.1903385 | 1498 | 0.0050863 | 4472.80009 | -14.478658 | -14.353517 | -14.481069 | -14.428356 |
| eGARCH | 0.0025043 | 2633 | 0.0030365 | 33.08998 | -6.506425 | -6.407679 | -6.507968 | -6.466732 |
| gjrGARCH | 0.0007881 | 3871 | 0.0020662 | 11.85352 | -6.490010 | -6.392866 | -6.491498 | -6.450963 |
| apARCH | 0.0073280 | 578 | 0.0138155 | 9400.26094 | -13.662422 | -13.549574 | -13.664418 | -13.617063 |
| iGARCH | 0.0013876 | 3871 | 0.0020659 | 11.80779 | -6.453708 | -6.383861 | -6.454512 | -6.425632 |
| csGARCH | 0.0013193 | 3871 | 0.0020660 | 11.79309 | -6.446913 | -6.336120 | -6.448822 | -6.402379 |
6.5.1.2 : Table summary
| Model | n |
|---|---|
| fGARCH.GARCH | 1 |
| fGARCH.NGARCH | 6 |
| fGARCH.ALLGARCH | 1 |
| eGARCH | 1 |
| apARCH | 1 |
| iGARCH | 1 |
6.5.1.3 : Table summary
## selected models' filtered closing price.
cl <- united.fx2 %>%
separate(Type, c('Cur', 'Type')) %>%
dplyr::filter(Type == 'Cl') %>% dplyr::select(-Cur, -Type)
acc <- cl %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 8.000000e-07 | 559 | 1.431130e-02 | 1.559246e-01 | -7.288436 | -7.206816 | -7.289503 | -7.255628 |
| USDAUD | fGARCH.GARCH | 8.000000e-07 | 559 | 1.431130e-02 | 1.558753e-01 | -7.288696 | -7.207077 | -7.289763 | -7.255888 |
| USDAUD | fGARCH.TGARCH | 3.100000e-06 | 559 | 1.431130e-02 | 4.728300e-01 | -7.096628 | -7.001354 | -7.098056 | -7.058331 |
| USDAUD | fGARCH.NGARCH | 1.250000e-05 | 559 | 1.431120e-02 | 1.121814e+04 | -25.853292 | -25.758019 | -25.854720 | -25.814995 |
| USDAUD | fGARCH.NAGARCH | 7.000000e-07 | 559 | 1.431130e-02 | 1.063490e+02 | -6.862443 | -6.767169 | -6.863871 | -6.824147 |
| USDAUD | fGARCH.GJRGARCH | 7.000000e-07 | 559 | 1.431130e-02 | 1.586611e-01 | -7.293262 | -7.197989 | -7.294690 | -7.254965 |
| USDAUD | gjrGARCH | 7.000000e-07 | 559 | 1.431130e-02 | 1.617046e-01 | -7.300716 | -7.205443 | -7.302145 | -7.262420 |
| USDAUD | iGARCH | 9.552767e+287 | 559 | -3.417806e+285 | 9.939089e+02 | -5.958293 | -5.890326 | -5.959052 | -5.930973 |
| USDAUD | csGARCH | 1.100000e-06 | 559 | 1.431130e-02 | 1.586346e-01 | -7.271781 | -7.162854 | -7.273623 | -7.227996 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 4.000000e-07 | 559 | 1.431130e-02 | 3.413732e-01 | -8.267597 | -8.184167 | -8.268702 | -8.234061 |
| USDEUR | fGARCH.GARCH | 4.000000e-07 | 559 | 1.431130e-02 | 3.409632e-01 | -8.267238 | -8.183808 | -8.268342 | -8.233702 |
| USDEUR | fGARCH.TGARCH | 1.300000e-06 | 559 | 1.431130e-02 | 5.897902e-01 | -8.152291 | -8.055208 | -8.153764 | -8.113267 |
| USDEUR | fGARCH.NGARCH | 2.400000e-06 | 559 | 1.431130e-02 | 9.114206e+03 | -23.208609 | -23.111526 | -23.210083 | -23.169586 |
| USDEUR | fGARCH.NAGARCH | 3.000000e-07 | 559 | 1.431130e-02 | 3.493310e-01 | -8.283230 | -8.186147 | -8.284703 | -8.244206 |
| USDEUR | fGARCH.GJRGARCH | 3.000000e-07 | 559 | 1.431130e-02 | 3.496629e-01 | -8.283745 | -8.186662 | -8.285219 | -8.244722 |
| USDEUR | gjrGARCH | 4.000000e-07 | 559 | 1.431130e-02 | 3.540859e-01 | -8.295254 | -8.198171 | -8.296727 | -8.256230 |
| USDEUR | iGARCH | 1.100000e-06 | 559 | 1.431130e-02 | 3.453162e-01 | -8.266395 | -8.196619 | -8.267186 | -8.238348 |
| USDEUR | csGARCH | 1.100000e-06 | 559 | 1.431130e-02 | 3.362058e-01 | -8.250495 | -8.139759 | -8.252390 | -8.205984 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 1.127189e-01 | -8.981649 | -8.902148 | -8.982680 | -8.949694 |
| USDGBP | fGARCH.GARCH | 2.000000e-07 | 559 | 1.431130e-02 | 1.123181e-01 | -8.982166 | -8.902665 | -8.983196 | -8.950210 |
| USDGBP | fGARCH.TGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 3.222055e-01 | -8.751631 | -8.658490 | -8.753013 | -8.714193 |
| USDGBP | fGARCH.NGARCH | 6.227218e+27 | 559 | -2.227985e+25 | 7.331325e+03 | -20.726300 | -20.633159 | -20.727683 | -20.688862 |
| USDGBP | fGARCH.NAGARCH | 0.000000e+00 | 559 | 1.431130e-02 | 8.933084e-01 | -8.960998 | -8.867857 | -8.962381 | -8.923561 |
| USDGBP | fGARCH.GJRGARCH | 0.000000e+00 | 559 | 1.431130e-02 | 1.179164e-01 | -8.999605 | -8.906464 | -9.000987 | -8.962167 |
| USDGBP | gjrGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 1.241116e-01 | -9.012987 | -8.919847 | -9.014370 | -8.975550 |
| USDGBP | iGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 1.116974e-01 | -8.984394 | -8.918532 | -8.985125 | -8.957921 |
| USDGBP | csGARCH | 1.000000e-07 | 559 | 1.431130e-02 | 1.113388e-01 | -8.963484 | -8.856703 | -8.965272 | -8.920564 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 3.600000e-06 | 559 | 1.431130e-02 | 4.833457e-01 | -7.474117 | -7.391001 | -7.475226 | -7.440707 |
| USDCHF | fGARCH.GARCH | 3.800000e-06 | 559 | 1.431130e-02 | 4.839503e-01 | -7.474806 | -7.391691 | -7.475915 | -7.441396 |
| USDCHF | fGARCH.TGARCH | 1.500000e-06 | 559 | 1.431130e-02 | 4.096568e-01 | -7.537571 | -7.440799 | -7.539047 | -7.498672 |
| USDCHF | fGARCH.NGARCH | 2.500000e-06 | 559 | 1.431130e-02 | 1.446917e+04 | -32.808316 | -32.711545 | -32.809793 | -32.769418 |
| USDCHF | fGARCH.NAGARCH | 1.800000e-06 | 559 | 1.431130e-02 | 5.051191e+01 | -6.827660 | -6.730889 | -6.829136 | -6.788761 |
| USDCHF | fGARCH.GJRGARCH | 2.500000e-06 | 559 | 1.431130e-02 | 4.534221e-01 | -7.526291 | -7.429520 | -7.527768 | -7.487393 |
| USDCHF | gjrGARCH | 2.200000e-06 | 559 | 1.431130e-02 | 4.533756e-01 | -7.547867 | -7.451096 | -7.549344 | -7.508969 |
| USDCHF | iGARCH | 3.800000e-06 | 559 | 1.431130e-02 | 5.381170e-01 | -7.452484 | -7.383024 | -7.453279 | -7.424564 |
| USDCHF | csGARCH | 3.600000e-06 | 559 | 1.431130e-02 | 4.904606e-01 | -7.458188 | -7.347761 | -7.460085 | -7.413800 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 3.000000e-07 | 559 | 1.431130e-02 | 1.966726e-01 | -7.991148 | -7.910425 | -7.992195 | -7.958700 |
| USDCAD | fGARCH.GARCH | 2.000000e-07 | 559 | 1.431130e-02 | 1.968368e-01 | -7.990829 | -7.910107 | -7.991876 | -7.958381 |
| USDCAD | fGARCH.TGARCH | 1.100000e-06 | 559 | 1.431130e-02 | 6.003772e-01 | -7.775149 | -7.680773 | -7.776554 | -7.737213 |
| USDCAD | fGARCH.NGARCH | 1.138994e+43 | 559 | -4.075114e+40 | 1.046825e+04 | -26.405445 | -26.311070 | -26.406851 | -26.367510 |
| USDCAD | fGARCH.NAGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 1.959558e-01 | -8.000013 | -7.905637 | -8.001418 | -7.962077 |
| USDCAD | fGARCH.GJRGARCH | 2.000000e-07 | 559 | 1.431130e-02 | 2.001156e-01 | -7.998766 | -7.904391 | -8.000172 | -7.960831 |
| USDCAD | gjrGARCH | 3.000000e-07 | 559 | 1.431130e-02 | 1.989161e-01 | -8.005552 | -7.911176 | -8.006957 | -7.967616 |
| USDCAD | iGARCH | 3.000000e-07 | 559 | 1.431130e-02 | 1.992656e-01 | -7.989905 | -7.922836 | -7.990649 | -7.962946 |
| USDCAD | csGARCH | 3.000000e-07 | 559 | 1.431130e-02 | 1.942810e-01 | -7.975787 | -7.867758 | -7.977604 | -7.932364 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 8.300000e-06 | 559 | 1.431120e-02 | 2.005993e-01 | -6.944040 | -6.854835 | -6.945293 | -6.908184 |
| USDCNY | fGARCH.GARCH | 8.100000e-06 | 559 | 1.431120e-02 | 2.004410e-01 | -6.944340 | -6.855135 | -6.945593 | -6.908484 |
| USDCNY | fGARCH.TGARCH | 9.400000e-06 | 559 | 1.431120e-02 | 7.839599e-01 | -6.722028 | -6.619180 | -6.723671 | -6.680688 |
| USDCNY | fGARCH.NGARCH | 1.880000e-05 | 559 | 1.431120e-02 | 1.217151e+03 | -9.067536 | -8.964689 | -9.069180 | -9.026197 |
| USDCNY | fGARCH.NAGARCH | 8.100000e-06 | 559 | 1.431120e-02 | 2.141826e-01 | -6.958927 | -6.856080 | -6.960570 | -6.917587 |
| USDCNY | fGARCH.GJRGARCH | 7.000000e-06 | 559 | 1.431120e-02 | 2.106660e-01 | -6.969452 | -6.866604 | -6.971095 | -6.928112 |
| USDCNY | gjrGARCH | 6.900000e-06 | 559 | 1.431120e-02 | 1.894846e-01 | -6.998676 | -6.895829 | -7.000319 | -6.957336 |
| USDCNY | iGARCH | 8.900000e-06 | 559 | 1.431120e-02 | 2.121785e-01 | -6.932317 | -6.856755 | -6.933233 | -6.901945 |
| USDCNY | csGARCH | 6.800000e-06 | 559 | 1.431120e-02 | 2.179735e-01 | -6.960187 | -6.843697 | -6.962273 | -6.913364 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 9.465900e-03 | 559 | 1.427740e-02 | 1.721053e-01 | 1.731319 | 1.818461 | 1.730089 | 1.766346 |
| USDJPY | fGARCH.GARCH | 9.324200e-03 | 559 | 1.427790e-02 | 1.719392e-01 | 1.731538 | 1.818680 | 1.730308 | 1.766564 |
| USDJPY | fGARCH.TGARCH | 6.421400e-03 | 559 | 1.428830e-02 | 1.861072e-01 | 1.735527 | 1.836312 | 1.733916 | 1.776037 |
| USDJPY | fGARCH.NGARCH | 2.850280e-02 | 559 | 1.420930e-02 | 8.977524e+03 | -16.272255 | -16.171471 | -16.273867 | -16.231745 |
| USDJPY | fGARCH.NAGARCH | 5.789800e-03 | 559 | 1.429060e-02 | 1.830579e-01 | 1.718799 | 1.819584 | 1.717188 | 1.759310 |
| USDJPY | fGARCH.GJRGARCH | 6.495300e-03 | 559 | 1.428800e-02 | 1.783422e-01 | 1.727660 | 1.828444 | 1.726048 | 1.768170 |
| USDJPY | gjrGARCH | 5.510200e-03 | 559 | 1.429160e-02 | 1.863184e-01 | 1.716339 | 1.817123 | 1.714727 | 1.756849 |
| USDJPY | iGARCH | 9.626200e-03 | 559 | 1.427680e-02 | 1.742753e-01 | 1.727553 | 1.801052 | 1.726651 | 1.757095 |
| USDJPY | csGARCH | 9.167800e-03 | 559 | 1.427850e-02 | 1.692019e-01 | 1.737118 | 1.851544 | 1.735071 | 1.783111 |
6.5.2.1A : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 1.354200e-03 | 3913 | 2.043800e-03 | 11.81143 | -6.459381 | -6.375847 | -6.460501 | -6.425804 |
| fGARCH.GARCH | 1.334000e-03 | 3913 | 2.043800e-03 | 11.81223 | -6.459505 | -6.375972 | -6.460625 | -6.425928 |
| fGARCH.TGARCH | 9.197000e-04 | 3913 | 2.044000e-03 | 11.69868 | -6.328538 | -6.231356 | -6.330027 | -6.289475 |
| fGARCH.NGARCH | 1.627135e+42 | 3913 | -8.316559e+38 | 9021.42422 | -22.048822 | -21.951640 | -22.050311 | -22.009759 |
| fGARCH.NAGARCH | 8.287000e-04 | 3913 | 2.044000e-03 | 33.99004 | -6.310639 | -6.213457 | -6.312127 | -6.271576 |
| fGARCH.GJRGARCH | 9.294000e-04 | 3913 | 2.044000e-03 | 11.84838 | -6.477637 | -6.380455 | -6.479126 | -6.438574 |
| gjrGARCH | 7.887000e-04 | 3913 | 2.044100e-03 | 11.85262 | -6.492102 | -6.394920 | -6.493591 | -6.453039 |
| iGARCH | 1.364681e+287 | 3913 | -6.975114e+283 | 153.67088 | -6.265177 | -6.195292 | -6.265982 | -6.237086 |
| csGARCH | 1.311500e-03 | 3913 | 2.043800e-03 | 11.79235 | -6.448972 | -6.338141 | -6.450882 | -6.404423 |
6.5.2.1B : Table summary
| Model | n |
|---|---|
| fGARCH.NGARCH | 3 |
| iGARCH | 1 |
6.5.2.1C : Table summary
## selected models' filtered closing price.
cl <- united.fx3 %>%
separate(Type, c('Cur', 'Type')) %>%
dplyr::filter(Type == 'Cl') %>% dplyr::select(-Cur, -Type)
acc <- cl %>%
ddply(.(.id, Model), summarise,
MSE = mean((Price.T1 - Price)^2),
n = length(Price),
AIC.MSE = (-2*MSE)/n+2*4/n,
MSE.AIC = mean((Akaike - mean(Akaike))^2),
Akaike = mean(Akaike),
Bayes = mean(Bayes),
Shibata = mean(Shibata),
Hannan.Quinn = mean(Hannan.Quinn)) %>%
tbl_df %>% mutate(MSE = round(MSE, 7))
| .id | Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|---|
| USD/AUD | |||||||||
| USDAUD | sGARCH | 0.0000007 | 488 | 0.0163934 | 1.640505e-01 | -7.265794 | -7.184917 | -7.266838 | -7.233285 |
| USDAUD | fGARCH.GARCH | 0.0000008 | 488 | 0.0163934 | 1.640095e-01 | -7.266065 | -7.185188 | -7.267109 | -7.233555 |
| USDAUD | fGARCH.TGARCH | 0.0000033 | 488 | 0.0163934 | 5.093595e-01 | -7.070468 | -6.975937 | -7.071870 | -7.032470 |
| USDAUD | fGARCH.NGARCH | 0.0000141 | 488 | 0.0163934 | 1.211134e+04 | -27.494174 | -27.399643 | -27.495576 | -27.456176 |
| USDAUD | fGARCH.NAGARCH | 0.0000006 | 488 | 0.0163934 | 1.217519e+02 | -6.775897 | -6.681366 | -6.777299 | -6.737899 |
| USDAUD | fGARCH.GJRGARCH | 0.0000007 | 488 | 0.0163934 | 1.668917e-01 | -7.270418 | -7.175887 | -7.271820 | -7.232420 |
| USDAUD | gjrGARCH | 0.0000007 | 488 | 0.0163934 | 1.701981e-01 | -7.277713 | -7.183183 | -7.279116 | -7.239716 |
| USDAUD | iGARCH | 0.0000008 | 488 | 0.0163934 | 1.638295e-01 | -7.271403 | -7.204180 | -7.272143 | -7.244382 |
| USDAUD | csGARCH | 0.0000010 | 488 | 0.0163934 | 1.668663e-01 | -7.248406 | -7.140223 | -7.250220 | -7.204921 |
| USD/CAD | |||||||||
| USDEUR | sGARCH | 0.0000004 | 488 | 0.0163934 | 3.043725e-01 | -8.194585 | -8.111886 | -8.195669 | -8.161343 |
| USDEUR | fGARCH.GARCH | 0.0000004 | 488 | 0.0163934 | 3.045893e-01 | -8.194634 | -8.111936 | -8.195718 | -8.161393 |
| USDEUR | fGARCH.TGARCH | 0.0000006 | 488 | 0.0163934 | 5.499310e-01 | -8.078199 | -7.981847 | -8.079649 | -8.039469 |
| USDEUR | fGARCH.NGARCH | 0.0000026 | 488 | 0.0163934 | 1.040528e+04 | -25.314306 | -25.217954 | -25.315756 | -25.275576 |
| USDEUR | fGARCH.NAGARCH | 0.0000003 | 488 | 0.0163934 | 3.158747e-01 | -8.212065 | -8.115713 | -8.213514 | -8.173335 |
| USDEUR | fGARCH.GJRGARCH | 0.0000003 | 488 | 0.0163934 | 3.164714e-01 | -8.212689 | -8.116337 | -8.214139 | -8.173960 |
| USDEUR | gjrGARCH | 0.0000003 | 488 | 0.0163934 | 3.237036e-01 | -8.225715 | -8.129363 | -8.227164 | -8.186985 |
| USDEUR | iGARCH | 0.0000004 | 488 | 0.0163934 | 3.089839e-01 | -8.196219 | -8.127174 | -8.196990 | -8.168465 |
| USDEUR | csGARCH | 0.0000004 | 488 | 0.0163934 | 3.002656e-01 | -8.180627 | -8.070622 | -8.182495 | -8.136409 |
| USD/CHF | |||||||||
| USDGBP | sGARCH | 0.0000002 | 488 | 0.0163934 | 9.945270e-02 | -8.937714 | -8.858980 | -8.938723 | -8.906067 |
| USDGBP | fGARCH.GARCH | 0.0000002 | 488 | 0.0163934 | 9.908220e-02 | -8.938328 | -8.859593 | -8.939337 | -8.906681 |
| USDGBP | fGARCH.TGARCH | 0.0000001 | 488 | 0.0163934 | 2.944775e-01 | -8.712794 | -8.620422 | -8.714153 | -8.675666 |
| USDGBP | fGARCH.NGARCH | 0.0000011 | 488 | 0.0163934 | 6.727908e+03 | -19.352385 | -19.260012 | -19.353743 | -19.315256 |
| USDGBP | fGARCH.NAGARCH | 0.0000000 | 488 | 0.0163934 | 9.892981e-01 | -8.911294 | -8.818922 | -8.912653 | -8.874166 |
| USDGBP | fGARCH.GJRGARCH | 0.0000000 | 488 | 0.0163934 | 1.050671e-01 | -8.955486 | -8.863113 | -8.956844 | -8.918357 |
| USDGBP | gjrGARCH | 0.0000001 | 488 | 0.0163934 | 1.112930e-01 | -8.968258 | -8.875885 | -8.969617 | -8.931129 |
| USDGBP | iGARCH | 0.0000000 | 488 | 0.0163934 | 9.884410e-02 | -8.941000 | -8.875904 | -8.941713 | -8.914834 |
| USDGBP | csGARCH | 0.0000001 | 488 | 0.0163934 | 9.819870e-02 | -8.919730 | -8.813718 | -8.921490 | -8.877119 |
| USD/CNY | |||||||||
| USDCHF | sGARCH | 0.0000039 | 488 | 0.0163934 | 4.442418e-01 | -7.423164 | -7.341108 | -7.424238 | -7.390180 |
| USDCHF | fGARCH.GARCH | 0.0000041 | 488 | 0.0163934 | 4.452317e-01 | -7.423984 | -7.341927 | -7.425058 | -7.391000 |
| USDCHF | fGARCH.TGARCH | 0.0000016 | 488 | 0.0163934 | 3.878747e-01 | -7.483775 | -7.388062 | -7.485212 | -7.445301 |
| USDCHF | fGARCH.NGARCH | 0.0000027 | 488 | 0.0163934 | 1.549129e+04 | -34.172671 | -34.076958 | -34.174108 | -34.134197 |
| USDCHF | fGARCH.NAGARCH | 0.0000020 | 488 | 0.0163934 | 5.751416e+01 | -6.692202 | -6.596489 | -6.693639 | -6.653728 |
| USDCHF | fGARCH.GJRGARCH | 0.0000024 | 488 | 0.0163934 | 4.206748e-01 | -7.474347 | -7.378635 | -7.475785 | -7.435874 |
| USDCHF | gjrGARCH | 0.0000024 | 488 | 0.0163934 | 4.277776e-01 | -7.493454 | -7.397741 | -7.494891 | -7.454981 |
| USDCHF | iGARCH | 0.0000040 | 488 | 0.0163934 | 4.999841e-01 | -7.399624 | -7.331224 | -7.400389 | -7.372130 |
| USDCHF | csGARCH | 0.0000039 | 488 | 0.0163934 | 4.514381e-01 | -7.407227 | -7.297859 | -7.409081 | -7.363265 |
| USD/EUR | |||||||||
| USDCAD | sGARCH | 0.0000002 | 488 | 0.0163934 | 2.033350e-01 | -7.965958 | -7.885746 | -7.966990 | -7.933716 |
| USDCAD | fGARCH.GARCH | 0.0000002 | 488 | 0.0163934 | 2.035859e-01 | -7.965874 | -7.885662 | -7.966906 | -7.933632 |
| USDCAD | fGARCH.TGARCH | 0.0000012 | 488 | 0.0163934 | 6.375395e-01 | -7.742662 | -7.648797 | -7.744050 | -7.704932 |
| USDCAD | fGARCH.NGARCH | 0.0000046 | 488 | 0.0163934 | 1.152224e+04 | -28.662802 | -28.568936 | -28.664189 | -28.625071 |
| USDCAD | fGARCH.NAGARCH | 0.0000002 | 488 | 0.0163934 | 2.029774e-01 | -7.974742 | -7.880877 | -7.976130 | -7.937012 |
| USDCAD | fGARCH.GJRGARCH | 0.0000002 | 488 | 0.0163934 | 2.075853e-01 | -7.973967 | -7.880102 | -7.975355 | -7.936237 |
| USDCAD | gjrGARCH | 0.0000003 | 488 | 0.0163934 | 2.058195e-01 | -7.980342 | -7.886477 | -7.981730 | -7.942612 |
| USDCAD | iGARCH | 0.0000003 | 488 | 0.0163934 | 2.064388e-01 | -7.964406 | -7.897847 | -7.965136 | -7.937652 |
| USDCAD | csGARCH | 0.0000003 | 488 | 0.0163934 | 2.010313e-01 | -7.950250 | -7.842731 | -7.952046 | -7.907031 |
| USD/GBP | |||||||||
| USDCNY | sGARCH | 0.0000082 | 488 | 0.0163934 | 1.791054e-01 | -6.895420 | -6.805153 | -6.896704 | -6.859137 |
| USDCNY | fGARCH.GARCH | 0.0000081 | 488 | 0.0163934 | 1.790114e-01 | -6.895816 | -6.805549 | -6.897100 | -6.859533 |
| USDCNY | fGARCH.TGARCH | 0.0000105 | 488 | 0.0163934 | 7.797819e-01 | -6.660423 | -6.556514 | -6.662102 | -6.618657 |
| USDCNY | fGARCH.NGARCH | 0.0000202 | 488 | 0.0163934 | 1.393683e+03 | -9.325252 | -9.221343 | -9.326930 | -9.283486 |
| USDCNY | fGARCH.NAGARCH | 0.0000082 | 488 | 0.0163934 | 1.937612e-01 | -6.910226 | -6.806317 | -6.911905 | -6.868460 |
| USDCNY | fGARCH.GJRGARCH | 0.0000071 | 488 | 0.0163934 | 1.910457e-01 | -6.922611 | -6.818702 | -6.924289 | -6.880845 |
| USDCNY | gjrGARCH | 0.0000070 | 488 | 0.0163934 | 1.701114e-01 | -6.954555 | -6.850646 | -6.956233 | -6.912789 |
| USDCNY | iGARCH | 0.0000090 | 488 | 0.0163934 | 1.895962e-01 | -6.881227 | -6.804601 | -6.882169 | -6.850427 |
| USDCNY | csGARCH | 0.0000067 | 488 | 0.0163934 | 1.955561e-01 | -6.911533 | -6.793982 | -6.913658 | -6.864283 |
| USD/JPY | |||||||||
| USDJPY | sGARCH | 0.0101300 | 488 | 0.0163519 | 1.659875e-01 | 1.774301 | 1.860556 | 1.773095 | 1.808971 |
| USDJPY | fGARCH.GARCH | 0.0100138 | 488 | 0.0163524 | 1.658045e-01 | 1.774532 | 1.860786 | 1.773326 | 1.809202 |
| USDJPY | fGARCH.TGARCH | 0.0068814 | 488 | 0.0163652 | 1.821559e-01 | 1.777820 | 1.877716 | 1.776235 | 1.817973 |
| USDJPY | fGARCH.NGARCH | 0.0312636 | 488 | 0.0162653 | 9.290068e+03 | -16.849968 | -16.750072 | -16.851553 | -16.809815 |
| USDJPY | fGARCH.NAGARCH | 0.0058185 | 488 | 0.0163696 | 1.776433e-01 | 1.762115 | 1.862011 | 1.760530 | 1.802267 |
| USDJPY | fGARCH.GJRGARCH | 0.0068951 | 488 | 0.0163652 | 1.721750e-01 | 1.771170 | 1.871066 | 1.769585 | 1.811323 |
| USDJPY | gjrGARCH | 0.0056445 | 488 | 0.0163703 | 1.797094e-01 | 1.760812 | 1.860708 | 1.759227 | 1.800965 |
| USDJPY | iGARCH | 0.0102985 | 488 | 0.0163512 | 1.680102e-01 | 1.770926 | 1.843539 | 1.770045 | 1.800113 |
| USDJPY | csGARCH | 0.0098545 | 488 | 0.0163531 | 1.633717e-01 | 1.779806 | 1.893344 | 1.777791 | 1.825442 |
6.5.2.2A : Table summary
| Model | MSE | n | AIC.MSE | MSE.AIC | Akaike | Bayes | Shibata | Hannan.Quinn |
|---|---|---|---|---|---|---|---|---|
| sGARCH | 0.0014491 | 3416 | 0.0023411 | 11.79039 | -6.415476 | -6.332462 | -6.416581 | -6.382108 |
| fGARCH.GARCH | 0.0014325 | 3416 | 0.0023411 | 11.79183 | -6.415738 | -6.332724 | -6.416843 | -6.382370 |
| fGARCH.TGARCH | 0.0009855 | 3416 | 0.0023413 | 11.68280 | -6.281500 | -6.184838 | -6.282972 | -6.242646 |
| fGARCH.NGARCH | 0.0044727 | 3416 | 0.0023393 | 9623.19741 | -23.024508 | -22.927846 | -23.025979 | -22.985654 |
| fGARCH.NAGARCH | 0.0008328 | 3416 | 0.0023414 | 37.16491 | -6.244902 | -6.148239 | -6.246373 | -6.206048 |
| fGARCH.GJRGARCH | 0.0009866 | 3416 | 0.0023413 | 11.83122 | -6.434050 | -6.337387 | -6.435521 | -6.395196 |
| gjrGARCH | 0.0008079 | 3416 | 0.0023414 | 11.83875 | -6.448461 | -6.351798 | -6.449932 | -6.409607 |
| iGARCH | 0.0014733 | 3416 | 0.0023411 | 11.78848 | -6.411850 | -6.342484 | -6.412642 | -6.383968 |
| csGARCH | 0.0014096 | 3416 | 0.0023411 | 11.77209 | -6.405424 | -6.295113 | -6.407314 | -6.361084 |
6.5.2.2B : Table summary
| Model | n |
|---|---|
6.5.2.2C : Table summary
I had optimised the mean.model but not yet optimise the variance.model, Binary.com Interview Q1 - Tick-Data-HiLo For Daily Trading (Blooper) has provides an example for GARCH(m,n) comparison while below are the papers studied on the optimal GARCH order.
Above article states that the task of jointly determining the ARMA-GARCH orders is difficult…
I set snorm as the default distribution from the comparison of ROI in Binary-Q19. rgarchdist - Distribution:Rugarch Distribution Functions list the available distribution function for rugarch.
Does anything NOT beat the GARCH(1,1)? had compared few GARCH models which are :
with four distributions, the Normal, Skew-Student (Fernandez and Steel version), Normal Inverse Gaussian (NIG) and Johnson’s SU (JSU). The conditional mean was based on an ARMA(2,1) model, while the GARCH order was set at (1,1) and (2,1), giving a total combination of 64 models. To create the rolling forecasts, the ugarchroll() was used…
The author concludes that the normality assumption does not realistically capture the observed market dynamics, and neither does the GARCH(1,1)-N model. There were few models which did not beat it in this application. In fact, higher order GARCH models were shown to provide significant out performance on a range of tail related measures, and distributions such as the NIG and JSU appeared to provide the most realistic representation of the observed dynamics.
The author proof that the matrix relationship10 among the distribution and models in order to get the best fit model. However there are couple of thesises proof that the best fit model for forex, stocks market is difference.
Here I skipped the distribution section due to above model comparison in section GARCH Models has compare the models… Binary.com Interview Q1 has compare the models as well.
norm for normal distribution.snorm for skew-normal distribution.std for student-t distribution.sstd for skew-student distribution.ged for generalized error distribution.sged for skew-generalized error distribution.nig for normal inverse gaussian distribution.ghyp for generalized hyperbolic distribution.jsu for Johnson’s SU distribution.The article Does anything NOT beat the GARCH(1,1)? using hybrid same with my previous paper Binary.com Interview Q1 where my paper test and choose it since it is best fit for gjrGARCH model.
GARCH模型中的ARMA(p,d,q)参数最优化 compare the accuracy of the model and the paper Binary.com Interview Q1 - Tick-Data-HiLo For Daily Trading (Blooper) states the wrong of the staking model in Binary.com Interview Q1 as I use the price as odds price without calculate the loss.11 However, here I try to review on paper Binary.com Interview Q1 to compare the accuracy of prediction.
In order to validate the accuracy of prediction, here I added this section to compare among the models. I added a mean mse for Hi and Lo in order to know the long term accuracy between Hi-Lo since an order stand upon the accuracy of both Hi and Lo. binary-Q1 Multivariate GARCH Models will be another study for both punter and banker.
## read files
fls <- list.files('data', patter = '.snorm.hybrid.rds$')
mds <- llply(fls, function(txt) {
tryCatch(readRDS(paste0('data/', txt)),
error = function(e) cat(paste0('data/', txt, ' error!\n')))
})
## data/fGARCH.ALLGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.AVGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NAGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.TGARCH.Mn.Cl.snorm.hybrid.rds error!
names(mds) <- str_replace_all(fls, '.rds', '')
## measure mse.
mds <- llply(names(mds), function(x) {
HiLo <- x %>% str_extract_all('Hi.Lo|Lo.Hi|Hi.Cl|Lo.Cl|Op.Hi|
Op.Lo|Op.Cl') %>% unlist
if (length(HiLo) > 0) {
dfm <- mds[[x]]
if (HiLo == 'Hi.Lo') {
dfm %<>% mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2),
mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique
} else if (HiLo == 'Lo.Hi') {
dfm %<>% mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2),
mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique
} else if (HiLo == 'Hi.Cl') {
dfm %<>% mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2),
mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique
} else if (HiLo == 'Lo.Cl') {
dfm %<>% mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2),
mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique
} else if (HiLo == 'Op.Hi') {
dfm %<>% mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2),
mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique
} else if (HiLo == 'Op.Lo') {
dfm %<>% mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2),
mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique
} else if (HiLo == 'Op.Cl') {
dfm %<>% mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2),
mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique
} else {
stop('No such option.')
}
dfm %<>% .[, -c(1:26)] %>% unique
}
})
names(mds) <- str_replace_all(fls, '.rds', '')
mds %<>% ldply
mds %>% mutate(mse.HiLo = (mse.Hi + mse.Lo)/2) %>%
kable(caption = 'Summary') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')
| .id | mse.Hi | mse.Lo | mse.Cl | mse.Op | mse.HiLo |
|---|---|---|---|---|---|
| csGARCH.Hi.Lo.snorm.hybrid | 8.862459e+156 | 6.305287e-01 | NA | NA | 4.431230e+156 |
| csGARCH.Lo.Hi.snorm.hybrid | 1.572061e+148 | 6.306860e-01 | NA | NA | 7.860305e+147 |
| fGARCH.GARCH.Hi.Lo.snorm.hybrid | 4.957576e-01 | 6.443517e-01 | NA | NA | 5.700547e-01 |
| fGARCH.GARCH.Lo.Hi.snorm.hybrid | 4.936336e-01 | 6.443517e-01 | NA | NA | 5.689927e-01 |
| fGARCH.GJRGARCH.Lo.Cl.snorm.hybrid | NA | 6.479395e-01 | 0.5550178 | NA | NA |
| fGARCH.GJRGARCH.Op.Cl.snorm.hybrid | NA | NA | 0.5550178 | 0.5727289 | NA |
| fGARCH.NGARCH.Hi.Lo.snorm.hybrid | 1.453179e+173 | 2.913652e+146 | NA | NA | 7.265897e+172 |
| fGARCH.NGARCH.Lo.Hi.snorm.hybrid | 9.098227e+122 | 2.319707e+03 | NA | NA | 4.549113e+122 |
| gjrGARCH.EWMA.est.Hi.Lo.snorm.hybrid | 2.038695e+144 | 6.470051e-01 | NA | NA | 1.019348e+144 |
| gjrGARCH.EWMA.est.Lo.Hi.snorm.hybrid | 3.024325e+77 | 6.470589e-01 | NA | NA | 1.512162e+77 |
| gjrGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid | 2.022071e+63 | 6.469073e-01 | NA | NA | 1.011035e+63 |
| gjrGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid | 1.238697e+143 | 6.470093e-01 | NA | NA | 6.193487e+142 |
| gjrGARCH.Hi.Cl.snorm.hybrid | 4.762089e+145 | NA | 0.5581871 | NA | NA |
| gjrGARCH.Hi.Lo.snorm.hybrid | 7.977139e+79 | 6.469860e-01 | NA | NA | 3.988569e+79 |
| gjrGARCH.Lo.Cl.snorm.hybrid | NA | 1.221226e+229 | 0.5581871 | NA | NA |
| gjrGARCH.Lo.Hi.snorm.hybrid | 4.901055e-01 | 6.469729e-01 | NA | NA | 5.685392e-01 |
| gjrGARCH.Op.Cl.snorm.hybrid | NA | NA | 0.5581871 | 0.5748052 | NA |
| gjrGARCH.Op.Hi.snorm.hybrid | 3.599090e+109 | NA | NA | 0.5746087 | NA |
| iGARCH.EWMA.est.Hi.Lo.snorm.hybrid | 4.957351e-01 | 6.556720e-01 | NA | NA | 5.757036e-01 |
| iGARCH.EWMA.est.Lo.Hi.snorm.hybrid | 8.558115e+73 | 6.556720e-01 | NA | NA | 4.279058e+73 |
| iGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid | 2.888561e+216 | 6.556720e-01 | NA | NA | 1.444280e+216 |
| iGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid | 4.958495e-01 | 6.556720e-01 | NA | NA | 5.757608e-01 |
| iGARCH.Hi.Lo.snorm.hybrid | 4.958608e-01 | 6.556720e-01 | NA | NA | 5.757664e-01 |
| iGARCH.Lo.Hi.snorm.hybrid | 4.957999e-01 | 6.556720e-01 | NA | NA | 5.757359e-01 |
| realGARCH.Hi.Lo.snorm.hybrid | 9.856535e+05 | 8.231377e+06 | NA | NA | 4.608515e+06 |
| realGARCH.Lo.Hi.snorm.hybrid | 9.856535e+05 | 8.231377e+06 | NA | NA | 4.608515e+06 |
| sGARCH.Hi.Lo.snorm.hybrid | 4.998315e-01 | 6.383346e-01 | NA | NA | 5.690830e-01 |
| sGARCH.Lo.Hi.snorm.hybrid | 4.958049e-01 | 6.383346e-01 | NA | NA | 5.670697e-01 |
Here I filtered the sd < 20% dataset as below.
## read files
fls <- list.files('data', patter = '.snorm.hybrid.rds$')
mds <- llply(fls, function(txt) {
tryCatch(readRDS(paste0('data/', txt)),
error = function(e) cat(paste0('data/', txt, ' error!\n')))
})
## data/fGARCH.ALLGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.AVGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NAGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.TGARCH.Mn.Cl.snorm.hybrid.rds error!
names(mds) <- str_replace_all(fls, '.rds', '')
## measure mse.
mds <- llply(names(mds), function(x) {
HiLo <- x %>% str_extract_all('Hi.Lo|Lo.Hi|Hi.Cl|Lo.Cl|Op.Hi|
Op.Lo|Op.Cl') %>% unlist
if (length(HiLo) > 0) {
dfm <- mds[[x]]
if (HiLo == 'Hi.Lo') {
dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.High),
se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0),
diff2 = abs(forClose/USDJPY.Low),
se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
) %>%
dplyr::filter(se1 != 1 & se2 != 1) %>%
mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2),
mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique
} else if (HiLo == 'Lo.Hi') {
dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Low),
se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0),
diff2 = abs(forClose/USDJPY.High),
se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
) %>%
dplyr::filter(se1 != 1 & se2 != 1) %>%
mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2),
mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique
} else if (HiLo == 'Hi.Cl') {
dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.High),
se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0),
diff2 = abs(forClose/USDJPY.Close),
se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
) %>%
dplyr::filter(se1 != 1 & se2 != 1) %>%
mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2),
mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique
} else if (HiLo == 'Lo.Cl') {
dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Low),
se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0),
diff2 = abs(forClose/USDJPY.Close),
se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
) %>%
dplyr::filter(se1 != 1 & se2 != 1) %>%
mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2),
mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique
} else if (HiLo == 'Op.Hi') {
dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Open),
se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0),
diff2 = abs(forClose/USDJPY.High),
se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
) %>%
dplyr::filter(se1 != 1 & se2 != 1) %>%
mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2),
mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique
} else if (HiLo == 'Op.Lo') {
dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Open),
se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0),
diff2 = abs(forClose/USDJPY.Low),
se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
) %>%
dplyr::filter(se1 != 1 & se2 != 1) %>%
mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2),
mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique
} else if (HiLo == 'Op.Cl') {
dfm %<>% mutate(diff1 = abs(Point.Forecast/USDJPY.Open),
se1 = ifelse(diff1 <= 0.8 | diff1 >= 1.25, 1, 0),
diff2 = abs(forClose/USDJPY.Close),
se2 = ifelse(diff2 <= 0.8 | diff2 >= 1.25, 1, 0)
) %>%
dplyr::filter(se1 != 1 & se2 != 1) %>%
mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2),
mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique
} else {
stop('No such option.')
}
dfm %<>% .[, -c(1:30)] %>% unique
}
})
names(mds) <- str_replace_all(fls, '.rds', '')
mds %<>% ldply
mds %>% mutate(mse.HiLo = (mse.Hi + mse.Lo)/2) %>%
kable(caption = 'Summary') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')
| .id | mse.Hi | mse.Lo | mse.Cl | mse.Op | mse.HiLo |
|---|---|---|---|---|---|
| csGARCH.Hi.Lo.snorm.hybrid | 2.0229955 | 0.6277246 | NA | NA | 1.3253601 |
| csGARCH.Lo.Hi.snorm.hybrid | 2.0196959 | 0.6328959 | NA | NA | 1.3262959 |
| fGARCH.GARCH.Hi.Lo.snorm.hybrid | 0.4957576 | 0.6443517 | NA | NA | 0.5700547 |
| fGARCH.GARCH.Lo.Hi.snorm.hybrid | 0.4936336 | 0.6443517 | NA | NA | 0.5689927 |
| fGARCH.GJRGARCH.Lo.Cl.snorm.hybrid | NA | 0.6479395 | 0.5550178 | NA | NA |
| fGARCH.GJRGARCH.Op.Cl.snorm.hybrid | NA | NA | 0.5550178 | 0.5727289 | NA |
| fGARCH.NGARCH.Hi.Lo.snorm.hybrid | 0.4907338 | 1.0560979 | NA | NA | 0.7734159 |
| fGARCH.NGARCH.Lo.Hi.snorm.hybrid | 119.9887775 | 0.7500664 | NA | NA | 60.3694219 |
| gjrGARCH.EWMA.est.Hi.Lo.snorm.hybrid | 0.4877976 | 0.6448733 | NA | NA | 0.5663354 |
| gjrGARCH.EWMA.est.Lo.Hi.snorm.hybrid | 0.4913398 | 0.6479219 | NA | NA | 0.5696308 |
| gjrGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid | 0.4855612 | 0.6294052 | NA | NA | 0.5574832 |
| gjrGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid | 0.4873248 | 0.6315175 | NA | NA | 0.5594211 |
| gjrGARCH.Hi.Cl.snorm.hybrid | 0.4903484 | NA | 0.5591785 | NA | NA |
| gjrGARCH.Hi.Lo.snorm.hybrid | 0.4853209 | 0.6294841 | NA | NA | 0.5574025 |
| gjrGARCH.Lo.Cl.snorm.hybrid | NA | 0.6479054 | 0.5577813 | NA | NA |
| gjrGARCH.Lo.Hi.snorm.hybrid | 0.4901055 | 0.6469729 | NA | NA | 0.5685392 |
| gjrGARCH.Op.Cl.snorm.hybrid | NA | NA | 0.5581871 | 0.5748052 | NA |
| gjrGARCH.Op.Hi.snorm.hybrid | 0.4897748 | NA | NA | 0.5756845 | NA |
| iGARCH.EWMA.est.Hi.Lo.snorm.hybrid | 0.4957351 | 0.6556720 | NA | NA | 0.5757036 |
| iGARCH.EWMA.est.Lo.Hi.snorm.hybrid | 0.4966432 | 0.6566751 | NA | NA | 0.5766591 |
| iGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid | 0.4966460 | 0.6552626 | NA | NA | 0.5759543 |
| iGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid | 0.4958495 | 0.6556720 | NA | NA | 0.5757608 |
| iGARCH.Hi.Lo.snorm.hybrid | 0.4958608 | 0.6556720 | NA | NA | 0.5757664 |
| iGARCH.Lo.Hi.snorm.hybrid | 0.4957999 | 0.6556720 | NA | NA | 0.5757359 |
| realGARCH.Hi.Lo.snorm.hybrid | 1163.6111434 | 188.6156300 | NA | NA | 676.1133867 |
| realGARCH.Lo.Hi.snorm.hybrid | 1163.6111434 | 188.6156300 | NA | NA | 676.1133867 |
| sGARCH.Hi.Lo.snorm.hybrid | 0.4998315 | 0.6383346 | NA | NA | 0.5690830 |
| sGARCH.Lo.Hi.snorm.hybrid | 0.4958049 | 0.6383346 | NA | NA | 0.5670697 |
Now I filtered the forecast price must be within highest and lowest price in order to made the order stand.
## read files
fls <- list.files('data', patter = '.snorm.hybrid.rds$')
mds <- llply(fls, function(txt) {
tryCatch(readRDS(paste0('data/', txt)),
error = function(e) cat(paste0('data/', txt, ' error!\n')))
})
## data/fGARCH.ALLGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.AVGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NAGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.NGARCH.Mn.Cl.snorm.hybrid.rds error!
## data/fGARCH.TGARCH.Mn.Cl.snorm.hybrid.rds error!
names(mds) <- str_replace_all(fls, '.rds', '')
## measure mse.
mds <- llply(names(mds), function(x) {
HiLo <- x %>% str_extract_all('Hi.Lo|Lo.Hi|Hi.Cl|Lo.Cl|Op.Hi|
Op.Lo|Op.Cl') %>% unlist
if (length(HiLo) > 0) {
dfm <- mds[[x]]
if (HiLo == 'Hi.Lo') {
dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High &
Point.Forecast >= USDJPY.Low &
forClose <= USDJPY.High &
forClose >= USDJPY.Low) %>%
mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2),
mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique
} else if (HiLo == 'Lo.Hi') {
dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High &
Point.Forecast >= USDJPY.Low &
forClose <= USDJPY.High &
forClose >= USDJPY.Low) %>%
mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2),
mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique
} else if (HiLo == 'Hi.Cl') {
dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High &
Point.Forecast >= USDJPY.Low &
forClose <= USDJPY.High &
forClose >= USDJPY.Low) %>%
mutate(mse.Hi = mean((Point.Forecast - USDJPY.High)^2),
mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique
} else if (HiLo == 'Lo.Cl') {
dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High &
Point.Forecast >= USDJPY.Low &
forClose <= USDJPY.High &
forClose >= USDJPY.Low) %>%
mutate(mse.Lo = mean((Point.Forecast - USDJPY.Low)^2),
mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique
} else if (HiLo == 'Op.Hi') {
dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High &
Point.Forecast >= USDJPY.Low &
forClose <= USDJPY.High &
forClose >= USDJPY.Low) %>%
mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2),
mse.Hi = mean((forClose - USDJPY.High)^2)) %>% unique
} else if (HiLo == 'Op.Lo') {
dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High &
Point.Forecast >= USDJPY.Low &
forClose <= USDJPY.High &
forClose >= USDJPY.Low) %>%
mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2),
mse.Lo = mean((forClose - USDJPY.Low)^2)) %>% unique
} else if (HiLo == 'Op.Cl') {
dfm %<>% dplyr::filter(Point.Forecast <= USDJPY.High &
Point.Forecast >= USDJPY.Low &
forClose <= USDJPY.High &
forClose >= USDJPY.Low) %>%
mutate(mse.Op = mean((Point.Forecast - USDJPY.Open)^2),
mse.Cl = mean((forClose - USDJPY.Close)^2)) %>% unique
} else {
stop('No such option.')
}
dfm %<>% .[, -c(1:26)] %>% unique
}
})
names(mds) <- str_replace_all(fls, '.rds', '')
mds %<>% ldply
mds %>% mutate(mse.HiLo = (mse.Hi + mse.Lo)/2) %>%
kable(caption = 'Summary') %>%
kable_styling(bootstrap_options = c('striped', 'hover', 'condensed', 'responsive')) %>%
scroll_box(width = '100%', height = '400px')
| .id | mse.Hi | mse.Lo | mse.Cl | mse.Op | mse.HiLo |
|---|---|---|---|---|---|
| csGARCH.Hi.Lo.snorm.hybrid | 0.1725682 | 0.6189147 | NA | NA | 0.3957415 |
| csGARCH.Lo.Hi.snorm.hybrid | 0.1754137 | 0.6303761 | NA | NA | 0.4028949 |
| fGARCH.GARCH.Hi.Lo.snorm.hybrid | 0.1925144 | 0.5379021 | NA | NA | 0.3652083 |
| fGARCH.GARCH.Lo.Hi.snorm.hybrid | 0.1925144 | 0.5379021 | NA | NA | 0.3652083 |
| fGARCH.GJRGARCH.Lo.Cl.snorm.hybrid | NA | 0.5372528 | 0.1295187 | NA | NA |
| fGARCH.GJRGARCH.Op.Cl.snorm.hybrid | NA | NA | 0.1299436 | 0.1249402 | NA |
| fGARCH.NGARCH.Hi.Lo.snorm.hybrid | 0.2272118 | 0.5121823 | NA | NA | 0.3696971 |
| fGARCH.NGARCH.Lo.Hi.snorm.hybrid | 0.2123187 | 0.4634484 | NA | NA | 0.3378836 |
| gjrGARCH.EWMA.est.Hi.Lo.snorm.hybrid | 0.1822257 | 0.5579749 | NA | NA | 0.3701003 |
| gjrGARCH.EWMA.est.Lo.Hi.snorm.hybrid | 0.1822257 | 0.5579749 | NA | NA | 0.3701003 |
| gjrGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid | 0.1822257 | 0.5579749 | NA | NA | 0.3701003 |
| gjrGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid | 0.1822257 | 0.5579749 | NA | NA | 0.3701003 |
| gjrGARCH.Hi.Cl.snorm.hybrid | 0.2704312 | NA | 0.1325796 | NA | NA |
| gjrGARCH.Hi.Lo.snorm.hybrid | 0.1822257 | 0.5579749 | NA | NA | 0.3701003 |
| gjrGARCH.Lo.Cl.snorm.hybrid | NA | 0.5373148 | 0.1373641 | NA | NA |
| gjrGARCH.Lo.Hi.snorm.hybrid | 0.1822257 | 0.5579749 | NA | NA | 0.3701003 |
| gjrGARCH.Op.Cl.snorm.hybrid | NA | NA | 0.1292683 | 0.1156056 | NA |
| gjrGARCH.Op.Hi.snorm.hybrid | 0.2381400 | NA | NA | 0.1411032 | NA |
| iGARCH.EWMA.est.Hi.Lo.snorm.hybrid | 0.1290527 | 0.5816668 | NA | NA | 0.3553598 |
| iGARCH.EWMA.est.Lo.Hi.snorm.hybrid | 0.1269647 | 0.5866267 | NA | NA | 0.3567957 |
| iGARCH.EWMA.fixed.Hi.Lo.snorm.hybrid | 0.1290527 | 0.5816668 | NA | NA | 0.3553598 |
| iGARCH.EWMA.fixed.Lo.Hi.snorm.hybrid | 0.1290527 | 0.5816668 | NA | NA | 0.3553598 |
| iGARCH.Hi.Lo.snorm.hybrid | 0.1290527 | 0.5816668 | NA | NA | 0.3553598 |
| iGARCH.Lo.Hi.snorm.hybrid | 0.1277353 | 0.5866267 | NA | NA | 0.3571810 |
| realGARCH.Hi.Lo.snorm.hybrid | 0.1321052 | 1.1086522 | NA | NA | 0.6203787 |
| realGARCH.Lo.Hi.snorm.hybrid | 0.1321052 | 1.1086522 | NA | NA | 0.6203787 |
| sGARCH.Hi.Lo.snorm.hybrid | 0.1054852 | 0.6143042 | NA | NA | 0.3598947 |
| sGARCH.Lo.Hi.snorm.hybrid | 0.1054852 | 0.6143042 | NA | NA | 0.3598947 |
Due to some unknown reason, the NGARCH and NAGARCH (and other models, some currencies as well.)12 always bias, therefore the AIC/BIC value and the mse value opposite site to made we hard to judge if it is good to fit. Fortunately I try to filter the bias where \(\sigma ≥ 20\%\) and count the number of occurance to pick the model.
Perhaps the other day will compare the matrix models fit with distribution and solver. The multivariate GARCH model is also on going.
There are a lot of time I waste just for verify and rerun the coding. ugarchroll function always interrupted after running few hours. The simulation wrote by me always interrupt as well, there are 14 GARCH models while I running 6 models at the meantime. ugarchroll for refit.windows = 'recrusive' cost me few days time while refit.windows = 'moving' cost me weeks time and all in 24 hours without any rest.
After get the MSE value and AIC value, I forced to debug the codes upon unexpected results especially bias. For example, the MSE value judge the best fit model but AIC and BIC judge as worst model. Here I also looking for some reference like AIC for MSE which applied AIC for compare the best MSE as introduced by a professor.
Below are the blooper (behind the scene) for GARCH模型中的ARMA(p,d,q)参数最优化 where I use almost a week to review and filter couple times.
This paper compares 14 models with 3 mthods but GARCH模型中的ARMA(p,d,q)参数最优化 only compares 2 models.
It’s useful to record some information about how your file was created.
| Category | session_info | Category | Sys.info |
|---|---|---|---|
| version | R version 3.5.1 (2018-07-02) | sysname | Windows |
| system | x86_64, mingw32 | release | 10 x64 |
| ui | RTerm | version | build 16299 |
| language | en | nodename | RSTUDIO-SCIBROK |
| collate | Japanese_Japan.932 | machine | x86-64 |
| tz | Asia/Tokyo | login | scibr |
| date | 2018-08-25 | user | scibr |
| Current time | 2018-08-25 23:30:34 JST | effective_user | scibr |
ARMA(p,d,q)参数最优化Powered by - Copyright® Intellectual Property Rights of Scibrokes®個人の経営企業
Only the solver=solnp stable but the other solvers not stable, the fluctuation of AIC value is quite high.↩
Due to some errors↩
tryCatch() might useful for llply() or else we can use for() to skip NULL or error result. Normally I will add cat() upon completion of one prediction to know the progress of whole simulation.↩
Markov Chain theory explain the statiscal predicton only can predict the next stage based on current stage. For example in soccer In-Play : 1-0 or 0-1 can be predicted during 0-0, the fit for 0-0 will not be usable anymore once there has scored. Similar concept with scoring intensity in Dixon & Robinson 1997, the armaOrder and arfima parameters optimised the preditive accuracy at every single stage.↩
gjrGARCH model generated highest ROI.↩
Therefore I skip [2nd Stage Model Comparison], my previous paper use 2nd stage parameter adjustment but noticed that the matrix relationship will correct.↩
VaR or other risk amount, the loss amount will be 1 for the exchange rate since \(\frac{100yen}{1}=100yen\) while I use the closed price as settled price if the forecast settled price has no within the range of Hi-Lo price within a trading day. There will be a leverage and slot unit required for financial market while a risk amount will be required for financial betting.↩
Kindly refer to section MSE, AIC and BIC.↩